Advanced Asymptotic Methods
暂无分享,去创建一个
[1] C. Meunier,et al. Multiphase Averaging for Classical Systems: With Applications To Adiabatic Theorems , 1988 .
[2] R. O'Malley. On the Asymptotic Solution of the Singularly Perturbed Boundary Value Problems Posed by Bohé , 2000 .
[3] A. Szeri,et al. Topology and resonances in a quasiperiodically forced oscillator , 2004 .
[4] Yuri Skrynnikov,et al. Solving Initial Value Problem by Matching Asymptotic Expansions , 2012, SIAM J. Appl. Math..
[5] D. Bainov,et al. Justification of the averaging method for a system of differential equations with fast and slow variables and with impulses , 1981 .
[6] Victor Martin-Mayor,et al. Field Theory, the Renormalization Group and Critical Phenomena , 1984 .
[7] Reinhard Schäfke,et al. Gevrey separation of fast and slow variables , 1996 .
[8] K. Roberts,et al. New Stokes’ line in WKB theory , 1982 .
[9] Paul C. Fife,et al. Boundary and interior transition layer phenomena for pairs of second-order differential equations☆ , 1976 .
[10] P. Hsieh. A turning point problem for a system of linear ordinary differential equations of the third order , 1965 .
[11] George A. Hagedorn,et al. A Time-Dependent Born–Oppenheimer Approximation with Exponentially Small Error Estimates , 2001 .
[12] Y. Sibuya,et al. Gevrey solutions of singularly perturbed differential equations , 2000 .
[13] J. Gillis,et al. Asymptotic Methods in the Theory of Non‐Linear Oscillations , 1963 .
[14] N. K. Rozov,et al. Differential Equations with Small Parameters and Relaxation Oscillations , 1980 .
[15] Cetin Cetinkaya,et al. Mode Localization in a Class of Multidegree-of-Freedom Nonlinear Systems with Cyclic Symmetry , 1993, SIAM J. Appl. Math..
[16] Asymptotic expansion for the solution of singularly perturbed delay differential equations , 2003 .
[17] R. G. Casten,et al. Basic Concepts Underlying Singular Perturbation Techniques , 1972 .
[18] Guy Métivier,et al. Averaging theorems for conservative systems and the weakly compressible Euler equations , 2003 .
[19] H. A. Kramers,et al. Wellenmechanik und halbzahlige Quantisierung , 1926 .
[20] Tim Kiemel,et al. Relative Phase Behavior of Two Slowly Coupled Oscillators , 1993, SIAM J. Appl. Math..
[21] Transition time analysis in singularly perturbed boundary value problems , 1995 .
[22] F. Verhulst,et al. Averaging Methods in Nonlinear Dynamical Systems , 1985 .
[23] Wiktor Eckhaus. Fundamental Concepts of Matching , 1994, SIAM Rev..
[24] É. Benoît,et al. Solutions surstables des équations différentielles complexes lentes-rapides à point tournant , 1998 .
[25] C. Howls. Exponential asymptotics and boundary-value problems: keeping both sides happy at all orders , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[26] L. Skinner. Uniform solution of boundary layer problems exhibiting resonance , 1987 .
[27] M. P. Williams. Another look at Ackerberg-O'Malley resonance , 1981 .
[28] Y. Kifer. Averaging and climate models , 2001 .
[29] P. Fife,et al. Existence of heteroclinic orbits for a corner layer problem in anisotropic interfaces , 2007, Advances in Differential Equations.
[30] De Groen. Spectral properties of second-order singularly perturbed boundary value problems with turning points , 1977 .
[31] J. Kevorkian,et al. Perturbation techniques for oscillatory systems with slowly varying coefficients , 1987 .
[32] Hinch. Perturbation Methods , 1991 .
[33] Eleftherios Kirkinis,et al. The Renormalization Group: A Perturbation Method for the Graduate Curriculum , 2012, SIAM Rev..
[34] J. Gervais,et al. WKB wave function for systems with many degrees of freedom: A unified view of solitons and pseudoparticles , 1977 .
[35] Leonid V. Kalachev,et al. The Boundary Function Method for Singular Perturbation Problems , 1995 .
[36] D. Reinelt,et al. Note on Logarithmic Switchback Terms in Regular and Singular Perturbation Expansions , 1984 .
[37] R. Marcus. Extension of the WKB method to wave functions and transition probability amplitudès (S-matrix) for inelastic or reactive collisions , 1970 .
[38] S. C. Persek,et al. Iterated averaging methods for systems of ordinary differential equations with a small parameter , 1978 .
[39] The approximate decomposition of exponential order of slow–fast motions in multifrequency systems , 2004 .
[40] W. Eckhaus. Asymptotic Analysis of Singular Perturbations , 1979 .
[41] R. Miura. The Korteweg–deVries Equation: A Survey of Results , 1976 .
[42] Multi-instantons and exact results I: Conjectures, WKB expansions, and instanton interactions , 2004, quant-ph/0501136.
[43] Shafic S. Oueini,et al. Dynamics of a Cubic Nonlinear Vibration Absorber , 1999 .
[44] I. Bright. Moving averages of ordinary differential equations via convolution , 2011 .
[45] Nigel Goldenfeld,et al. Selection, stability and renormalization , 1994 .
[46] Hui-Hui Dai,et al. Asymptotic Bifurcation Solutions for Compressions of a Clamped Nonlinearly Elastic Rectangle: Transition Region and Barrelling to a Corner-like Profile , 2009, SIAM J. Appl. Math..
[47] L. Long. Uniformly-valid asymptotic solutions to the Orr-Sommerfeld equation using multiple scales , 1987 .
[48] A. K. Bajaj,et al. On the Method of Averaging, Integral Manifolds and Systems with Symmetry , 1985 .
[49] B. Willner,et al. Uniform Asymptotic Solutions for Linear Second Order Ordinary Differential Equations with Turning Points: Formal Theory , 1977 .
[50] Robert M. Miura,et al. Singular Perturbation Analysis of Boundary Value Problems for Differential-Difference Equations , 1982 .
[51] I. Bright. Tight estimates for general averaging applied to almost-periodic differential equations , 2009 .
[52] Ali Nadim,et al. Coupled pulsation and translation of two gas bubbles in a liquid , 2001, Journal of Fluid Mechanics.
[53] William L. Kath. Necessary conditions for sustained reentry roll resonance , 1983 .
[54] C. Hunter,et al. On Lagerstrom's model of slow incompressible viscous flow , 1990 .
[55] On averaged and normal form equations , 1995 .
[56] Existence and stability of periodic motion under higher order averaging , 1986 .
[57] Hayato Chiba. Reduction of weakly nonlinear parabolic partial differential equations , 2013, 1302.0562.
[58] W. Eckhaus. Matched Asymptotic Expansions and Singular Perturbations , 1973 .
[59] On the Approximation of Double Limits by Single Limits and the Kaplun Extension Theorem , 1967 .
[60] Jan Awrejcewicz,et al. Asymptotic approaches in nonlinear dynamics , 1996 .
[61] Two-variable expansions and singular perturbation problems. , 1969 .
[62] Peter Szmolyan,et al. Asymptotic expansions using blow-up , 2005 .
[63] Joe H. Chow,et al. Singular perturbation analysis of systems with sustained high frequency oscillations , 1978, Autom..
[64] Xiaobiao Lin. Shadowing lemma and singularly perturbed boundary value problems , 1989 .
[65] Y. Sibuya. Formal solutions of a linear ordinary differential equation of the nth order at a turning point. , 1962 .
[66] F. Casas,et al. Unitary transformations depending on a small parameter , 2012, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[67] J. R. E. O’Malley. Singular perturbation methods for ordinary differential equations , 1991 .
[68] C. Meunier,et al. Multiphase Averaging for Classical Systems , 1988 .
[69] Lindsay A. Skinner. Singular Perturbation Theory , 2011 .
[70] J. Saut,et al. Well-Posedness and averaging of NLS with time-periodic dispersion management , 2012, Advances in Differential Equations.
[71] R. Haberman,et al. The Modulated Phase Shift for Strongly Nonlinear, Slowly Varying, and Weakly Damped Oscillators , 1988 .
[72] A. Macgillivray. A Method for Incorporating Transcendentally Small Terms into the Method of Matched Asymptotic Expansions , 1997 .
[73] Chuang Liu,et al. Scaling and Renormalization , 2002 .
[74] Emmanuel Frénod,et al. Application of the averaging method to the gyrokinetic plasma , 2007, Asymptot. Anal..
[75] Vladimir Gaitsgory,et al. Multiscale Singularly Perturbed Control Systems: Limit Occupational Measures Sets and Averaging , 2002, SIAM J. Control. Optim..
[76] S. Kordyukova. Approximate Group Analysis and Multiple Time Scales Method for the Approximate Boussinesq Equation , 2006 .
[77] J. Murdock. Perturbations: Theory and Methods , 1987 .
[78] Keith Promislow,et al. The semistrong limit of multipulse interaction in a thermally driven optical system , 2008 .
[79] J. Keller,et al. Loss of boundary conditions in the asymptotic solution of linear ordinary differential equations, II boundary value problems , 1968 .
[80] L. Brillouin,et al. La mécanique ondulatoire de Schrödinger; une méthode générale de resolution par approximations successives , 1926 .
[81] Y. Sibuya. Asymptotic solutions of a system of linear ordinary differential equations containing a parameter. , 1962 .
[82] P. Miller. Applied asymptotic analysis , 2006 .
[83] C. Comstock. The Poincaré–Lighthill Perturbation Technique and Its Generalizations , 1972 .
[84] N. Goldenfeld. Lectures On Phase Transitions And The Renormalization Group , 1972 .
[85] A B Vasil'eva. THE DEVELOPMENT OF THE THEORY OF ORDINARY DIFFERENTIAL EQUATIONS WITH A SMALL PARAMETER MULTIPLYING THE HIGHEST DERIVATIVE DURING THE PERIOD 1966-1976 , 1976 .
[86] George Esq. Green,et al. On the Motion of Waves in a variable canal of small depth and width , 1838 .
[87] Richard Haberman,et al. Averaging methods for the phase shift of arbitrarily perturbed strongly nonlinear oscillators with an application to capture , 1991 .
[88] Kenneth R. Meyer,et al. AVERAGING AND BIFURCATIONS IN SYMMETRIC SYSTEMS , 1977 .
[89] H. Bremmer,et al. The W.K.B. approximation as the first term of a geometric-optical series , 1951 .
[90] A. Kiselev,et al. Absolutely continuous spectrum for one-dimensional Schrodinger operators with slowly decaying potentials: Some optimal results , 1997, math/9706221.
[91] Jean Zinn-Justin,et al. Phase transitions and renormalization group , 2007 .
[92] J. Sanders,et al. Limit cycles in the Josephson equations , 1986 .
[93] R. O'Malley,et al. Deriving amplitude equations for weakly-nonlinear oscillators and their generalizations , 2006 .
[94] Ferdinand Verhulst,et al. A Metaphor for Adiabatic Evolution to Symmetry , 1995, SIAM J. Appl. Math..
[95] Iyer,et al. Black-hole normal modes: A WKB approach. I. Foundations and application of a higher-order WKB analysis of potential-barrier scattering. , 1987, Physical review. D, Particles and fields.
[96] Zvi Artstein,et al. Averaging of time-varying differential equations revisited , 2007 .
[97] Modification of the method of boundary functions for singularly perturbed partial differential equations , 1993 .
[98] P. Holmes,et al. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.
[99] Y. Sibuya. A Theorem Concerning Uniform Simplification at a Transition Point and the Problem of Resonance , 1981 .
[100] Robert E. O'Malley,et al. Examples Illustrating the Use of Renormalization Techniques for Singularly Perturbed Differential Equations , 2009 .
[101] M. Canalis-Durand. Solution formelle Gevrey d'une équation singulièrement perturbée , 1994 .
[102] Vladimir Gaitsgory,et al. Averaging of three time scale singularly perturbed control systems , 2001 .
[103] M. Newman,et al. Renormalization Group Analysis of the Small-World Network Model , 1999, cond-mat/9903357.
[104] Applying the dual operator formalism to derive the zeroth-order boundary function of the plasma-sheath equation , 2006 .
[105] P. A. Lagerstrom,et al. Matched Asymptotic Expansions , 1988 .
[106] F. W. J. Olver,et al. Error bounds for the Liouville–Green (or WKB) approximation , 1961, Mathematical Proceedings of the Cambridge Philosophical Society.
[107] Steven Weinberg,et al. Lectures on Quantum Mechanics: HISTORICAL INTRODUCTION , 2012 .
[108] Classification of resonant equations , 2004 .
[109] Jan Awrejcewicz,et al. Introduction to Asymptotic Methods , 2006 .
[110] J. Cahn,et al. Analysis of a corner layer problem in anisotropic interfaces , 2005 .
[111] Grigorios A. Pavliotis,et al. Multiscale Methods: Averaging and Homogenization , 2008 .
[112] A. Kiselev,et al. WKB and Spectral Analysis¶of One-Dimensional Schrödinger Operators¶with Slowly Varying Potentials , 2001 .
[113] F. Howes,et al. Nonlinear Singular Perturbation Phenomena: Theory and Applications , 1984 .
[114] C. Bender,et al. WKB analysis of -symmetric Sturm–Liouville problems , 2012, 1201.1234.
[115] Naoufel Ben Abdallah,et al. Time averaging for the strongly confined nonlinear Schrödinger equation, using almost-periodicity , 2008 .
[116] B. Matkowsky,et al. Singular Perturbations of Bifurcations , 1977 .
[117] G. Papamikos,et al. WKB approach applied to 1D time-dependent nonlinear Hamiltonian oscillators , 2012 .
[118] L. A. Skinner. Note on the Lagerstrom Singular Perturbation Models , 1981 .
[119] J. Cole,et al. Multiple Scale and Singular Perturbation Methods , 1996 .
[120] Johan Grasman,et al. A Variational Approach to Singularly Perturbed Boundary Value Problems for Ordinary and Partial Differential Equations with Turning Points , 1976 .
[121] D. L. Bosley. An Improved Matching Procedure for Transient Resonance Layers in Weakly Nonlinear Oscillatory Systems , 1996, SIAM J. Appl. Math..
[122] Michael E. Fisher,et al. The renormalization group in the theory of critical behavior , 1974 .
[123] S. Trofimchuk,et al. Krylov-Bogolyubov averaging of asymptotically autonomous differential equations , 2004 .
[124] Mark Levi,et al. Geometry and physics of averaging with applications , 1999 .
[125] R. McKelvey. The solutions of second order linear ordinary differential equations about a turning point of order two , 1955 .
[126] Oono,et al. Renormalization group theory for global asymptotic analysis. , 1994, Physical review letters.
[127] A. Macgillivray,et al. Asymptotic analysis of the peeling-off point of a French duck , 1994 .
[128] M. Krol,et al. On the averaging method in nearly time-periodic advection-diffusion problems , 1991 .
[129] Overstability: towards a global study , 1998 .
[130] L. Skinner. Matched expansion solutions of the first-order turning point problem , 1994 .
[131] Christof Sparber,et al. Mathematical and computational methods for semiclassical Schrödinger equations* , 2011, Acta Numerica.
[132] J. Féjoz. Averaging the Planar Three-Body Problem in the Neighborhood of Double Inner Collisions , 2001 .
[133] L. Rubenfeld. On a Derivative-Expansion Technique and Some Comments on Multiple Scaling in the Asymptotic Approximation of Solutions of Certain Differential Equations , 1978 .
[134] P. Fife,et al. Analysis of the heteroclinic connection in a singularly perturbed system arising from the study of crystalline grain boundaries , 2006 .
[135] J. Mesquita,et al. Non-periodic averaging principles for measure functional differential equations and functional dynamic equations on time scales involving impulses , 2013 .
[136] S. C. Persek,et al. Iterated averaging for periodic systems with hidden multiscale slow times. , 1984 .
[137] W. Eckhaus,et al. Theory and Applications of Singular Perturbations , 1982 .
[138] Evans M. Harrell. The Complex WKB Method for Nonlinear Equations 1: Linear Theory (Victor P. Maslov) , 1996, SIAM Rev..
[139] J. Cardy. Scaling and Renormalization in Statistical Physics , 1996 .
[140] M. Freidlin,et al. Geometric optics approach to reaction-diffusion equations , 1986 .
[141] Richard H. Rand,et al. Topics in Nonlinear Dynamics with Computer Algebra , 1994 .
[142] WKB-type approximations for second-order differential equations in C*-algebras , 1996 .
[143] Robert E. O'Malley,et al. A New Renormalization Method for the Asymptotic Solution of Weakly Nonlinear Vector Systems , 2003, SIAM J. Appl. Math..
[144] A. Fruchard,et al. ON COMBINED ASYMPTOTIC EXPANSIONS IN SINGULAR PERTURBATIONS , 2002 .
[145] V. A. Plotnikov,et al. Averaging of quasidifferential equations with fast and slow variables , 1998 .
[146] Robert E. O'Malley,et al. Singularly Perturbed Linear Two-Point Boundary Value Problems , 2008, SIAM Rev..
[147] Carmen Chicone,et al. Phase-Locked Loops, Demodulation, and Averaging Approximation Time-Scale Extensions , 2013, SIAM J. Appl. Dyn. Syst..
[148] John P. Boyd,et al. The Devil's Invention: Asymptotic, Superasymptotic and Hyperasymptotic Series , 1999 .
[149] Robert M. Miura,et al. Singular Perturbation Analysis of Boundary-Value Problems for Differential-Difference Equations. VI. Small Shifts with Rapid Oscillations , 1994, SIAM J. Appl. Math..
[150] Roger Temam,et al. Renormalization group method applied to the primitive equations , 2005 .
[151] Robert Krasny,et al. A Hybrid Asymptotic-Finite Element Method for Stiff Two-Point Boundary Value Problems , 1983 .
[152] J. Liouville. Troisième mémoire sur le développement des fonctions ou parties de fonctions en séries dont les divers termes sont assujettis à satisfaire à une même équation différentielle du second ordre, contenant un paramètre variable. , 1837 .
[153] J. Sanders. On the Fundamental Theorem of Averaging , 1983 .
[154] S. L. Woodruff. A uniformly-valid asymptotic solution to a matrix system of ordinary differential equations and a proof of its validity , 1995 .
[155] C. Comstock. On Lighthill’s Method of Strained Coordinates , 1968 .
[156] E. M. de Jager,et al. Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type , 1966 .
[157] Alexander Its,et al. A Riemann-Hilbert approach to asymptotic problems arising in the theory of random matrix models, and also in the theory of integrable statistical mechanics , 1997 .
[158] G. Ermentrout,et al. Analysis of neural excitability and oscillations , 1989 .
[159] H. Scott Dumas,et al. First-Order Averaging Principles for Maps with Applications to Accelerator Beam Dynamics , 2004, SIAM J. Appl. Dyn. Syst..
[160] Improved Nth order averaging theory for periodic systems , 1990 .
[161] Ovidiu Costin,et al. Asymptotics and Borel Summability , 2008 .
[162] S. Hastings,et al. Asymptotic behaviour of solutions of a similarity equation for laminar flows in channels with porous walls , 1992 .
[163] M. Berry,et al. Slow non-Hermitian cycling: exact solutions and the Stokes phenomenon , 2011 .
[164] Jan A. Sanders. On the Passage through Resonance , 1979 .
[165] Edward L. Reiss,et al. A new asymptotic method for jump phenomena , 1980 .
[166] K. Wilson. The renormalization group: Critical phenomena and the Kondo problem , 1975 .
[167] J. Baillieul,et al. Global Dynamics of a Rapidly Forced Cart and Pendulum , 1997 .
[168] A. Fisher,et al. The Theory of Critical Phenomena: An Introduction to the Renormalization Group , 1992 .
[169] Numerical study of oscillatory solutions of the gas-dynamic equations , 1991 .
[170] A. Doelman,et al. Quasi-periodically forced nonlinear Helmholtz oscillators , 2002 .
[171] François Golse,et al. Multiphase averaging for generalized flows on manifolds , 1994 .
[172] K. Wilson. The renormalization group and critical phenomena , 1983 .
[173] Exponential averaging for Hamiltonian evolution equations , 2002 .
[174] A note on Kaplun limits and double asymptotics , 1972 .
[175] P. Jakobsen,et al. Introduction to the method of multiple scales , 2013, 1312.3651.
[176] A. Macgillivray. The existence of an overlap domain for a singular perturbation problem , 1979 .
[177] Ali H. Nayfeh. The Method of Multiple Scales , 2007 .
[178] Chris J. Budd. Asymptotics of Multibump Blow-up Self-Similar Solutions of the Nonlinear Schrödinger Equation , 2002, SIAM J. Appl. Math..
[179] Steven A. Orszag,et al. Asymptotic methods and perturbation theory , 1999 .
[180] M. M. Dodson,et al. Averaging in multifrequency systems , 1989 .
[181] PETER A. BRAZA,et al. The Bifurcation Structure of the Holling--Tanner Model for Predator-Prey Interactions Using Two-Timing , 2003, SIAM J. Appl. Math..
[182] J. R. E. O’Malley. On Nonlinear Singularly Perturbed Initial Value Problems , 1988 .
[183] I. Moroz. Amplitude expansions and normal forms in a model for thermohaline convection , 1986 .
[184] K. Wilson,et al. The Renormalization group and the epsilon expansion , 1973 .
[185] B. Hall. Quantum Theory for Mathematicians , 2013 .
[186] Richard Haberman,et al. Standard form and a method of averaging for strongly nonlinear oscillatory dispersive traveling waves , 1991 .
[187] P. Fife. Transition layers in singular perturbation problems , 1974 .
[188] David A. Edwards,et al. An Alternative Example of the Method of Multiple Scales , 2000, SIAM Rev..
[189] G. Grammel. On Nonlinear Control Systems with Multiple Time Scales , 2004 .
[190] M. Canalis-Durand,et al. Monomial summability and doubly singular differential equations , 2007 .
[191] A. Macgillivray. On the switchback term in the asymptotic expansion of a model singular perturbation problem , 1980 .
[192] R. Konoplya. Quasinormal behavior of the D -dimensional Schwarzschild black hole and the higher order WKB approach , 2003 .
[193] L. Koralov,et al. Averaging of incompressible flows on two-dimensional surfaces , 2012 .
[194] Hayato Chiba,et al. Extension and Unification of Singular Perturbation Methods for ODEs Based on the Renormalization Group Method , 2009, SIAM J. Appl. Dyn. Syst..
[195] Yuri Kifer,et al. L2 Diffusion Approximation for Slow Motion in Averaging , 2003 .
[196] J. R. E. O’Malley. Shock and Transition Layers for Singularly Perturbed Second-Order Vector Systems , 1983 .
[197] H. Demiray. Multiple time scale formalism and its application to long water waves , 2010 .
[198] Shui-Nee Chow,et al. Integral averaging and bifurcation , 1977 .
[199] C. Bender,et al. Matched Asymptotic Expansions: Ideas and Techniques , 1988 .
[200] Rigorous WKB for finite-order linear recurrence relations with smooth coefficients , 2006, math/0608413.
[201] Annick Lesne,et al. Renormalization Methods - Critical Phenomena, Chaos, Fractal Structures , 1998 .
[202] Zaida Luthey-Schulten,et al. Determining the stability of genetic switches: explicitly accounting for mRNA noise. , 2011, Physical review letters.
[203] Discretization in the method of averaging , 1991 .
[204] A. Voros. Zeta-regularization for exact-WKB resolution of a general 1D Schrödinger equation , 2012, 1202.3100.
[205] André Deprit,et al. Canonical transformations depending on a small parameter , 1969 .
[206] N. Berglund,et al. The Averaged Dynamics of the Hydrogen Atom in Crossed Electric and Magnetic Fields as a Perturbed Kepler Problem , 2000, nlin/0007018.
[207] N. D. Bruijn. Asymptotic methods in analysis , 1958 .
[208] Zvi Artstein,et al. Young Measure Approach to Computing Slowly Advancing Fast Oscillations , 2008, Multiscale Model. Simul..
[209] D. Gilsinn. The Method of Averaging and Domains of Stability for Integral Manifolds , 1975 .
[210] C. Ou,et al. Shooting Method for Nonlinear Singularly Perturbed Boundary‐Value Problems , 2004 .
[211] Forman A. Williams,et al. Chain-Branching Explosions in Mixing Layers , 1999, SIAM J. Appl. Math..
[212] A. Nayfeh. Introduction To Perturbation Techniques , 1981 .
[213] S. Woodruff. The Use of an lnvariance Condition in the Solution of Multiple‐Scale Singular Perturbation Problems: Ordinary Differential Equations , 1993 .
[214] R. Haberman. Phase Shift Modulations for Stable, Oscillatory, Traveling, Strongly Nonlinear Waves , 1991 .
[215] Solution of reduced equations derived with singular perturbation methods. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.
[216] V. Bakhtin. Averaging in multifrequency systems , 1986 .
[217] P. Fatou,et al. Sur le mouvement d'un système soumis à des forces à courte période , 1928 .
[218] M. Berry,et al. High-order classical adiabatic reaction forces: slow manifold for a spin model , 2010 .
[219] M. Kouritzin. Averaging for Fundamental Solutions of Parabolic Equations , 1997 .
[220] A. D. MacGillivray. ON A MODEL EQUATION OF LAGERSTROM , 1978 .
[221] E. M. de Jager,et al. The theory of singular perturbations , 1996 .
[222] Stephen C. Persek. Hierarchies of Iterated Averages for Systems of Ordinary Differential Equations with a Small Parameter , 1981 .
[223] A remark on singular perturbation methods , 1985 .
[224] R. Estrada,et al. A distributional theory for asymptotic expansions , 1994 .
[225] G. Grammel. Limits of nonlinear discrete-time control systems with fast subsystems , 1999 .
[226] J. Mozo-Fernández,et al. Multisummability of Formal Solutions of Singular Perturbation Problems , 2002 .
[227] V. Trenogin. THE DEVELOPMENT AND APPLICATIONS OF THE ASYMPTOTIC METHOD OF LYUSTERNIK AND VISHIK , 1970 .
[228] Daniel O'Malley,et al. Two-scale renormalization-group classification of diffusive processes. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.
[229] Stable manifolds in the method of averaging , 1988 .
[230] A. Neishtadt. The separation of motions in systems with rapidly rotating phase , 1984 .
[231] J. Henrard. On a perturbation theory using Lie transforms , 1970 .
[232] S. Hastings,et al. A boundary value problem with multiple solutions from the theory of laminar flow , 1992 .
[233] Y. B. Fu,et al. WKB Method with Repeated Roots and Its Application to the Buckling Analysis of an Everted Cylindrical Tube , 2002, SIAM J. Appl. Math..
[234] Charles Knessl. On the Distribution of the Maximum Number of Broken Machines for the Repairman Problem , 1994, SIAM J. Appl. Math..
[235] R. O'Malley,et al. A Survey in Mathematics for Industry: Two-timing and matched asymptotic expansions for singular perturbation problems , 2011, European Journal of Applied Mathematics.
[236] Donald R. Smith. The Multivariable Method in Singular Perturbation Analysis , 1975 .
[237] R. O'Malley,et al. On singular singularly perturbed initial value problems , 1989 .
[238] J. Keller,et al. Uniform asymptotic solutions of second order linear ordinary differential equations with turning points , 1970 .
[239] C. Schroer. First Order Adiabatic Approximation for a Class of Classical Slow-Fast Systems with Ergodic Fast Dynamics , 1999 .
[240] H. Gingold,et al. Asymptotic Solutions of a Hamiltonian System in Intervals with Several Turning Points , 1988 .
[241] Jan A. Sanders. Asymptotic Approximations and Extension of Time-Scales , 1980 .
[242] Hayato Chiba,et al. C1 Approximation of Vector Fields Based on the Renormalization Group Method , 2008, SIAM J. Appl. Dyn. Syst..
[243] D. Wollkind. Singular Perturbation Techniques: A Comparison of the Method of Matched Asymptotic Expansions with that of Multiple Scales , 1977 .
[244] Dmitry Pelinovsky,et al. Averaging of Dispersion-Managed Solitons: Existence and Stability , 2003, SIAM J. Appl. Math..
[245] Y. Sibuya. Simplification of a linear ordinary differential equation of the nth order at a turning point , 1963 .
[246] Differentiability and its asymptotic analysis for nonlinear singularly perturbed boundary value problem , 2008 .
[247] C. Schmeiser,et al. Asymptotic analysis of singular singularly perturbed boundary value problems , 1986 .
[248] Karsten Matthies,et al. Time-Averaging under Fast Periodic Forcing of Parabolic Partial Differential Equations: Exponential Estimates , 2001 .
[249] Anthony Harkin,et al. Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations , 2008 .
[250] Chiang C. Mei,et al. On slowly-varying Stokes waves , 1970, Journal of Fluid Mechanics.
[251] Gregory A. Kriegsman,et al. Bifurcation in classical bipolar transistor oscillator circuits , 1989 .
[252] Rémi Carles,et al. (Semi)Classical Limit of the Hartree Equation with Harmonic Potential , 2005, SIAM J. Appl. Math..
[253] M. Ghil,et al. Non-Hamiltonian perturbations of integrable systems and resonance trapping , 1992 .
[254] Matching principles and composite expansions , 1977 .
[255] S. Dobrokhotov,et al. On various averaging methods for a nonlinear oscillator with slow time-dependent potential and a nonconservative perturbation , 2010 .
[256] W. Sarlet. On a common derivation of the averaging method and the two-timescale method , 1978 .
[257] John Bryce McLeod,et al. An Elementary Approach to a Model Problem of Lagerstrom , 2009, SIAM J. Math. Anal..
[258] B. Attili. Numerical treatment of singularly perturbed two point boundary value problems exhibiting boundary layers , 2011 .
[259] W. D. Evans,et al. PARTIAL DIFFERENTIAL EQUATIONS , 1941 .
[260] William L. Kath. Conditions for sustained resonance. II , 1983 .
[261] Georgi S. Medvedev,et al. Reduction of a model of an excitable cell to a one-dimensional map , 2005 .
[262] T. Gamelin. Complex Analysis , 2001 .
[263] Fuqin Sun. LIFE SPAN OF BLOW-UP SOLUTIONS FOR HIGHER-ORDER SEMILINEAR PARABOLIC EQUATIONS , 2010 .
[264] Composite asymptotic expansions and turning points of singularly perturbed ordinary differential equations , 2010 .
[265] Robert M. Miura,et al. Singular Perturbation Analysis of Boundary Value Problems for Differential-Difference Equations. V. Small Shifts with Layer Behavior , 1994, SIAM J. Appl. Math..
[266] Lawrence M. Perko,et al. Higher order averaging and related methods for perturbed periodic and quasi-periodic systems , 1969 .
[267] Philip Holmes,et al. Repeated Resonance and Homoclinic Bifurcation in a Periodically Forced Family of Oscillators , 1984 .
[268] Huang Guan. An averaging theorem for a perturbed KdV equation , 2013 .
[269] Dmitry V. Treschev,et al. An averaging method for Hamiltonian systems, exponentially close to integrable ones. , 1996, Chaos.
[270] Jeffrey Rauch,et al. Hyperbolic Partial Differential Equations and Geometric Optics , 2012 .
[271] James M. Hyman,et al. Stability, Relaxation, and Oscillation of Biodegradation Fronts , 2000, SIAM J. Appl. Math..
[272] C. Frenzen,et al. A review of the multiple scale and reductive perturbation methods for deriving uncoupled nonlinear evolution equations , 1985 .
[273] A. Neishtadt. On Averaging in Two-Frequency Systems with Small Hamiltonian and Much Smaller Non-Hamiltonian Perturbations , 2003 .
[274] Claudia Negulescu,et al. WKB-Based Schemes for the Oscillatory 1D Schrödinger Equation in the Semiclassical Limit , 2011, SIAM J. Numer. Anal..
[275] M. Janowicz. Method of multiple scales in quantum optics , 2003 .
[276] Leonid V. Kalachev,et al. A One-Dimensional Reaction/Diffusion System with a Fast Reaction☆ , 1997 .
[277] F. Chaplais,et al. Averaging and deterministic optimal control , 1987 .
[278] B. Willner,et al. Uniform asymptotic solutiion for a linear ordinary differential equation with one μ-th order turning point: Analytic theory , 1976 .
[279] Gregor Wentzel,et al. Eine Verallgemeinerung der Quantenbedingungen für die Zwecke der Wellenmechanik , 1926 .
[280] K. Schneider,et al. Global behavior and asymptotic reduction of a chemical kinetics system with continua of equilibria , 2005 .
[281] L. E. Fraenkel. On the method of matched asymptotic expansions , 1969 .
[282] Tere M. Seara,et al. Adiabatic invariant of the harmonic oscillator, complex matching and resurgence , 1998 .
[283] de Ppn Pieter Groen,et al. The nature of resonance in a singular perturbation problem of turning point type , 1980 .
[284] J. Norris,et al. Averaging over fast variables in the fluid limit for Markov chains: Application to the supermarket model with memory , 2010, 1001.0895.
[285] OPEN PROBLEM: Convergence, nonconvergence and adiabatic transitions in fully coupled averaging , 2008 .
[286] Leonid Fridman,et al. Slow periodic motions with internal sliding modes in variable structure systems , 2002 .
[287] S. Iyer,et al. Black-Hole Normal Modes: a WKB Approach , 1987 .
[288] H. Jeffreys. On Certain Approximate Solutions of Lineae Differential Equations of the Second Order , 1925 .
[289] Yuri Kifer,et al. Averaging in dynamical systems and large deviations , 1992 .
[290] John P. Boyd,et al. Hyperasymptotics and the Linear Boundary Layer Problem: Why Asymptotic Series Diverge , 2005, SIAM Rev..
[291] Athanassios S. Fokas,et al. Proof of some asymptotic results for a model equation for low Reynolds number flow , 1978 .
[292] Rémi Carles,et al. Semi-Classical Analysis For Nonlinear Schrodinger Equations , 2008 .
[293] L. Rubenfeld. The Passage of Weakly Coupled Nonlinear Oscillators through Internal Resonance , 1977 .
[294] N. Berglund,et al. Noise-Induced Phenomena in Slow-Fast Dynamical Systems: A Sample-Paths Approach , 2005 .
[295] Validity of the multiple scale method for very long intervals , 1996 .
[296] Hongxue Cai,et al. Radial Structure of Traveling Waves in the Inner Ear , 2003, SIAM J. Appl. Math..
[297] R. O'Malley,et al. Boundary Layer Problems Exhibiting Resonance , 1970 .
[298] G. Ermentrout,et al. Multiple pulse interactions and averaging in systems of coupled neural oscillators , 1991 .
[299] R. Shankar. Renormalization group approach to interacting fermions , 1994 .
[300] Joseph E. Flaherty,et al. Singularly perturbed boundary value problems for nonlinear systems, including a challenging problem for a nonlinear beam , 1982 .
[301] Robert M. Miura,et al. Application of a Nonlinear WKB Method to the Korteweg–DeVries Equation , 1974 .
[302] J. Morrison,et al. Comparison of the Modified Method of Averaging and the Two Variable Expansion Procedure , 1966 .
[303] E. Reiss. On Multivariable Asymptotic Expansions , 1971 .
[304] Simon Rosenblat,et al. On the asymptotic solution of the lagerstrom model equation , 1975 .
[305] C. Caroli,et al. Diffusion in a bistable potential: A systematic WKB treatment , 1979 .
[306] David E. Gilsinn,et al. A HIGH ORDER GENERALIZED METHOD OF AVERAGING , 1982 .
[307] A. Majda. Introduction to PDEs and Waves in Atmosphere and Ocean , 2003 .
[308] R. Bobryk. Closure method and asymptotic expansions for linear stochastic systems , 2007 .
[309] The Renormalized Two‐Scale Method , 2004 .
[310] Y. Kifer. Averaging principle for fully coupled dynamical systems and large deviations , 2004, Ergodic Theory and Dynamical Systems.
[311] Y. Sibuya. The Gevrey Asymptotics in the Case of Singular Perturbations , 2000 .
[312] F. Hoppensteadt. Analysis of Some Problems Having Matched Asymptotic Expansion Solutions , 1975 .
[313] Yuri A. Godin,et al. On the Determination of the Boundary Impedance from the Far Field Pattern , 2010, SIAM J. Appl. Math..
[314] Jens Lorenz,et al. On the existence of slow manifolds for problems with different timescales , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.
[315] F. A. Howes,et al. Nonlinear Singular Perturbation Phenomena , 1984 .
[316] On a Boundary Value Problem for a Nonlinear Differential Equation with a Small Parameter , 1969 .
[317] R. H. Good,et al. A WKB-Type Approximation to the Schrödinger Equation , 1953 .
[318] Oono,et al. Renormalization group and singular perturbations: Multiple scales, boundary layers, and reductive perturbation theory. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[319] Surstabilité pour une équation différentielle analytique en dimension un , 1990 .
[320] A. Nayfeh,et al. The method of multiple scales and non-linear dispersive waves , 1971, Journal of Fluid Mechanics.
[321] Clark Robinson,et al. Sustained Resonance for a Nonlinear System with Slowly Varying Coefficients , 1983 .
[322] Vimal Singh,et al. Perturbation methods , 1991 .
[323] Ali H. Nayfeh,et al. Resolving Controversies in the Application of the Method of Multiple Scales and the Generalized Method of Averaging , 2005 .
[324] A. B. Vasil’eva. ASYMPTOTIC BEHAVIOUR OF SOLUTIONS TO CERTAIN PROBLEMS INVOLVING NON-LINEAR DIFFERENTIAL EQUATIONS CONTAINING A?SMALL PARAMETER MULTIPLYING THE HIGHEST DERIVATIVES , 1963 .
[325] Angelo Luongo,et al. On the Reconstitution Problem in the Multiple Time-Scale Method , 1999 .
[326] Kenneth R. Meyer,et al. Geometric Averaging of Hamiltonian Systems: Periodic Solutions, Stability, and KAM Tori , 2011, SIAM Journal on Applied Dynamical Systems.