A perfect in phase FD algorithm for problems in quantum chemistry

Our research pays attention to the deployment of newly algorithm which is useful on quantum chemical problems.

[1]  H. De Meyer,et al.  Properties and implementation of ρ-Adams methods based on mixed-type interpolation , 1995 .

[2]  J. M. Franco.  Stability of explicit ARKN methods for perturbed oscillators , 2005 .

[3]  Jesús Vigo-Aguiar,et al.  A Parallel ODE Solver Adapted to Oscillatory Problems , 2004, The Journal of Supercomputing.

[4]  T. E. Simos,et al.  A Modified Runge-Kutta-Nystr¨ om Method by using Phase Lag Properties for the Numerical Solution of Orbital Problems , 2013 .

[5]  Theodore E. Simos,et al.  On modified Runge-Kutta trees and methods , 2011, Comput. Math. Appl..

[6]  Zhongcheng Wang,et al.  A new kind of discretization scheme for solving a two-dimensional time-independent Schrödinger equation , 2009, Comput. Phys. Commun..

[7]  A. D. Raptis,et al.  Exponential and Bessel fitting methods for the numerical solution of the Schrödinger equation , 1987 .

[8]  A. C. Allison,et al.  Exponential-fitting methods for the numerical solution of the schrodinger equation , 1978 .

[9]  T. E. Simos,et al.  A finite difference pair with improved phase and stability properties , 2017, Journal of Mathematical Chemistry.

[10]  J. M. Franco,et al.  High-order P-stable multistep methods , 1990 .

[11]  M. M. Chawla,et al.  An explicit sixth-order method with phase-lag of order eight for y ″= f ( t , y ) , 1987 .

[12]  J. Lambert,et al.  Symmetric Multistip Methods for Periodic Initial Value Problems , 1976 .

[13]  Zacharoula Kalogiratou,et al.  Exponentially fitted symplectic Runge-Kutta-Nyström methods , 2012 .

[14]  A. D. Raptis,et al.  A variable step method for the numerical integration of the one-dimensional Schrödinger equation , 1985 .

[15]  T. E. Simos,et al.  A new high algebraic order efficient finite difference method for the solution of the Schrödinger equation , 2017 .

[16]  T. Simos,et al.  Explicit hybrid six–step, sixth order, fully symmetric methods for solving  y ″ = f (x,y) , 2019, Mathematical Methods in the Applied Sciences.

[17]  J. M. Franco,et al.  Accuracy and linear stability of RKN methods for solving second-order stiff problems , 2009 .

[18]  Fatheah A. Hendi,et al.  P-Stable Higher Derivative Methods with Minimal Phase-Lag for Solving Second Order Differential Equations , 2011, J. Appl. Math..

[19]  M. M. Chawla,et al.  Non-dissipative extended one-step methods for oscillatory problems , 1998, Int. J. Comput. Math..

[20]  Xinyuan Wu,et al.  A trigonometrically fitted explicit hybrid method for the numerical integration of orbital problems , 2007, Appl. Math. Comput..

[21]  Tom E. Simos,et al.  A finite-difference method for the numerical solution of the Schro¨dinger equation , 1997 .

[22]  H. V. Vyver.  Efficient one-step methods for the Schrodinger equation , 2008 .

[23]  Moawwad E. A. El-Mikkawy,et al.  Families of Runge-Kutta-Nystrom Formulae , 1987 .

[24]  J. Martín-Vaquero,et al.  Exponential fitting BDF-Runge-Kutta algorithms , 2008, Comput. Phys. Commun..

[25]  J. M. Franco.  New methods for oscillatory systems based on ARKN methods , 2006 .

[26]  A. Raptis.  Exponential-fitting methods for the numerical integration of the fourth-order differential equation yIV+f·y=g , 2005, Computing.

[27]  Higinio Ramos,et al.  Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations , 2003 .

[28]  John P. Coleman.  Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine , 1989 .

[29]  J. Dormand,et al.  A family of embedded Runge-Kutta formulae , 1980 .

[30]  L.Gr. Ixaru,et al.  CP methods for the Schrödinger equation , 2000 .

[31]  Alexander B. Pacheco.  Introduction to Computational Chemistry , 2011 .

[32]  A. D. Raptis.  On the numerical solution of the Schrödinger equation , 1981 .

[33]  T. E. Simos,et al.  Exponentially fitted Runge-Kutta methods for the numerical solution of the Schrödinger equation and related problems , 2000 .

[34]  Alexander Dalgarno,et al.  Thermal scattering of atoms by homonuclear diatomic molecules , 1963, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[35]  Theodore E. Simos.  Optimizing a Hybrid Two-Step Method for the Numerical Solution of the Schrödinger Equation and Related Problems with Respect to Phase-Lag , 2012, J. Appl. Math..

[36]  M. M. Chawla,et al.  High-accuracy P-stable Methods for y″ = f(t, y) , 1985 .

[37]  A. Leach.  Molecular Modelling: Principles and Applications , 1996 .

[38]  Luis Rández,et al.  Explicit exponentially fitted two-step hybrid methods of high order for second-order oscillatory IVPs , 2016, Appl. Math. Comput..

[39]  Theodore E. Simos,et al.  A parametric symmetric linear four-step method for the efficient integration of the Schrödinger equation and related oscillatory problems , 2012, J. Comput. Appl. Math..

[40]  Jesús Vigo-Aguiar,et al.  Exponential fitted Gauss, Radau and Lobatto methods of low order , 2008, Numerical Algorithms.

[41]  M. Chawla,et al.  Singly-implicit stabilized extended one-step methods for second-order initial-value problems with oscillating solutions , 1999 .

[42]  T. E. Simos,et al.  A low computational cost eight algebraic order hybrid method with vanished phase-lag and its first, second, third and fourth derivatives for the approximate solution of the Schrödinger equation , 2015, Journal of Mathematical Chemistry.

[43]  G. Vanden Berghe,et al.  Exponentially-fitted Obrechkoff methods for second-order differential equations , 2006 .

[44]  José M. Ferrándiz,et al.  A General Procedure For the Adaptation of Multistep Algorithms to the Integration of Oscillatory Problems , 1998 .

[45]  An Optimized Symmetric 8-Step Semi-Embedded Predictor-Corrector Method for IVPs with Oscillating Solutions , 2013 .

[46]  Manuel Calvo,et al.  Sixth-order symmetric and symplectic exponentially fitted Runge-Kutta methods of the Gauss type , 2009 .

[47]  J. M. Franco.  Exponentially fitted symplectic integrators of RKN type for solving oscillatory problems , 2007, Comput. Phys. Commun..

[48]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[49]  T. Simos,et al.  A Runge–Kutta type implicit high algebraic order two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of coupled differential equations arising from the Schrödinger equation , 2015, Journal of Mathematical Chemistry.

[50]  J. M. Franco.  Runge–Kutta–Nyström methods adapted to the numerical integration of perturbed oscillators , 2002 .

[51]  Theodore E. Simos,et al.  Trigonometrical fitting conditions for two derivative Runge-Kutta methods , 2017, Numerical Algorithms.

[52]  Guido Vanden Berghe,et al.  Exponential-fitted four-step methods for , 1998, Int. J. Comput. Math..

[53]  T. Monovasilis,et al.  New fifth‐order two‐derivative Runge‐Kutta methods with constant and frequency‐dependent coefficients , 2019, Mathematical Methods in the Applied Sciences.

[54]  T. E. Simos,et al.  Trigonometric–fitted hybrid four–step methods of sixth order for solving y′′(x)=f(x,y) , 2018, Mathematical Methods in the Applied Sciences.

[55]  T. E. Simos,et al.  An efficient and economical high order method for the numerical approximation of the Schrödinger equation , 2017, Journal of Mathematical Chemistry.

[56]  J. Coleman,et al.  Analysis of a family of Chebyshev methods for y ′′ =f x,y , 1992 .

[57]  Manuel Calvo,et al.  Symmetric and symplectic exponentially fitted Runge-Kutta methods of high order , 2010, Comput. Phys. Commun..

[58]  M. M. Chawla,et al.  Intervals of periodicity and absolute stability of explicit nyström methods fory″=f(x,y) , 1981 .

[59]  Tom Lyche,et al.  Chebyshevian multistep methods for ordinary differential equations , 1972 .

[60]  Hans Van de Vyver.  Phase-fitted and amplification-fitted two-step hybrid methods for y˝= f ( x,y ) , 2007 .

[61]  Hans Van de Vyver,et al.  Frequency evaluation for exponentially fitted Runge-Kutta methods , 2005 .

[62]  Ch. Tsitouras,et al.  Trigonometric fitted, eighth‐order explicit Numerov‐type methods , 2018 .

[63]  M. Rizea.  Exponential fitting method for the time-dependent Schrödinger equation , 2010 .

[64]  L.Gr. Ixaru,et al.  Numerov method maximally adapted to the Schro¨dinger equation , 1987 .

[65]  T. E. Simos,et al.  A Runge–Kutta type crowded in phase algorithm for quantum chemistry problems , 2019, Journal of Mathematical Chemistry.

[66]  T. E. Simos,et al.  Fitted modifications of classical Runge‐Kutta pairs of orders 5(4) , 2018 .

[67]  Zhongcheng Wang,et al.  Arbitrarily precise numerical solutions of the one-dimensional Schrödinger equation , 2009, Comput. Phys. Commun..

[68]  Richard B. Bernstein,et al.  Quantum Mechanical (Phase Shift) Analysis of Differential Elastic Scattering of Molecular Beams , 1960 .

[69]  T. E. Simos,et al.  Explicit, two‐stage, sixth‐order, hybrid four‐step methods for solving y′′(x)=f(x,y) , 2018, Mathematical Methods in the Applied Sciences.

[70]  P. Atkins,et al.  Molecular Quantum Mechanics , 1970 .

[71]  Beatrice Paternoster,et al.  Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday , 2012, Comput. Phys. Commun..

[72]  L.Gr. Ixaru.  The numerov method and singular potentials , 1987 .

[73]  S. Tremaine,et al.  Symmetric Multistep Methods for the Numerical Integration of Planetary Orbits , 1990 .

[74]  T. E. Simos,et al.  Phase‐fitted, six‐step methods for solving x′′  =  f(t,x) , 2019, Mathematical Methods in the Applied Sciences.

[75]  L. Brugnano,et al.  Hamiltonian Boundary Value Methods ( Energy Preserving Discrete Line Integral Methods ) 1 2 , 2009 .

[76]  T. E. Simos,et al.  Construction of Exponentially Fitted Symplectic Runge–Kutta–Nyström Methods from Partitioned Runge–Kutta Methods , 2014, Mediterranean Journal of Mathematics.

[77]  T. E. Simos,et al.  A new multistage multistep full in phase algorithm with optimized characteristics for problems in chemistry , 2019, Journal of Mathematical Chemistry.

[78]  Yongming Dai,et al.  An improved trigonometrically fitted P-stable Obrechkoff method for periodic initial-value problems , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[79]  T. E. Simos,et al.  Construction of Exponentially Fitted Symplectic Runge–Kutta–Nyström Methods from Partitioned Runge–Kutta Methods , 2016 .

[80]  R. Thomas,et al.  Phase properties of high order, almostP-stable formulae , 1984 .

[81]  Zhongcheng Wang,et al.  Highly-accurate ground state energies of the He atom and the He-like ions by Hartree SCF calculation with Obrechkoff method , 2008, Comput. Phys. Commun..

[82]  Zhongcheng Wang.  Obrechkoff one-step method fitted with Fourier spectrum for undamped Duffing equation , 2006, Comput. Phys. Commun..

[83]  M. M. Chawla,et al.  Families of two-step fourth order P-stable methods for second oder differential equations , 1986 .

[84]  A. Konguetsof.  Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation , 2010 .

[85]  J. M. Franco,et al.  Some procedures for the construction of high-order exponentially fitted Runge-Kutta-Nyström methods of explicit type , 2013, Comput. Phys. Commun..

[86]  Theodore E. Simos,et al.  Construction of an optimized explicit Runge-Kutta-Nyström method for the numerical solution of oscillatory initial value problems , 2011, Comput. Math. Appl..

[87]  H. De Meyer,et al.  Weights of the exponential fitting multistep algorithms for first-order ODEs , 2001 .

[88]  Manuel Calvo,et al.  On some new low storage implementations of time advancing Runge-Kutta methods , 2012, J. Comput. Appl. Math..

[89]  Liviu Gr. Ixaru,et al.  P-stability and exponential-fitting methods for y″″ = f(x, y) , 1996 .

[90]  Theodore E. Simos,et al.  A new approach on the construction of trigonometrically fitted two step hybrid methods , 2016, J. Comput. Appl. Math..

[91]  J. Lambert.  Numerical Methods for Ordinary Differential Systems: The Initial Value Problem , 1991 .

[92]  T. E. Simos,et al.  A multistage two-step fraught in phase scheme for problems in mathematical chemistry , 2019, Journal of Mathematical Chemistry.

[93]  M. Rizea,et al.  Four step methods for y ′′ =f x,y , 1997 .

[94]  Hans Van de Vyver,et al.  An explicit Numerov-type method for second-order differential equations with oscillating solutions , 2007, Comput. Math. Appl..

[95]  Zhongcheng Wang.  Trigonometrically-fitted method for a periodic initial value problem with two frequencies , 2006, Comput. Phys. Commun..

[96]  Zhongcheng Wang.  Trigonometrically-fitted method with the Fourier frequency spectrum for undamped Duffing equation , 2006, Comput. Phys. Commun..

[97]  Mitsunori Ogihara,et al.  On the Reducibility of Sets Inside NP to Sets with Low Information Content , 2004 .

[98]  Theodore E. Simos,et al.  An optimized two-step hybrid block method for solving general second order initial-value problems , 2015, Numerical Algorithms.

[99]  Beny Neta,et al.  P-stable high-order super-implicit and Obrechkoff methods for periodic initial value problems , 2007, Comput. Math. Appl..

[100]  H. De Meyer,et al.  Exponentially fitted variable two-step BDF algorithm for first order ODEs☆ , 2003 .

[101]  M H Chawla,et al.  A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value , 1986 .

[102]  A. Konguetsof.  A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation , 2011 .

[103]  T. E. Simos,et al.  Fitted modifications of Runge‐Kutta pairs of orders 6(5) , 2018, Mathematical Methods in the Applied Sciences.

[104]  Haiqing Yan,et al.  The various order explicit multistep exponential fitting for systems of ordinary differential equations , 2004 .

[105]  Hans Van de Vyver,et al.  A symplectic exponentially fitted modified Runge–Kutta–Nyström method for the numerical integration of orbital problems , 2005 .

[106]  M. Rizea,et al.  Comparison of some four-step methods for the numerical solution of the Schrödinger equation , 1985 .

[107]  A. D. Raptis,et al.  A high order method for the numerical integration of the one-dimensional Schrödinger equation , 1984 .

[108]  Xinyuan Wu,et al.  A trigonometrically fitted explicit Numerov-type method for second-order initial value problems with oscillating solutions , 2008 .

[109]  Theodore E. Simos,et al.  High order closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the Schrödinger equation , 2009, Appl. Math. Comput..

[110]  J. M. Franco,et al.  Trigonometrically fitted nonlinear two-step methods for solving second order oscillatory IVPs , 2014, Appl. Math. Comput..

[111]  H. Meyer,et al.  EXPFIT4 - A FORTRAN program for the numerical solution of systems of nonlinear second-order initial-value problems. , 1997 .

[112]  Theodore E. Simos,et al.  A family of high-order multistep methods with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation , 2011, Comput. Math. Appl..

[113]  T. E. Simos.  New Stable Closed Newton-Cotes Trigonometrically Fitted Formulae for Long-Time Integration , 2012 .

[114]  H. Meyer,et al.  Four-step exponential-fitted methods for nonlinear physical problems , 1997 .

[115]  T. E. Simos,et al.  A three-stages multistep teeming in phase algorithm for computational problems in chemistry , 2019, Journal of Mathematical Chemistry.

[116]  Theodore E. Simos,et al.  A new family of symmetric linear four-step methods for the efficient integration of the Schrödinger equation and related oscillatory problems , 2012, Appl. Math. Comput..

[117]  A. Konguetsof.  A generator of families of two-step numerical methods with free parameters and minimal phase-lag , 2017, Journal of Mathematical Chemistry.

[118]  T. E. Simos,et al.  Optimization as a function of the phase-lag order of nonlinear explicit two-step P-stable method for linear periodic IVPs , 2009 .

[119]  Chenglian Liu,et al.  Hybrid Numerov-Type Methods with Coefficients Trained to Perform Better on Classical Orbits , 2019, Bulletin of the Malaysian Mathematical Sciences Society.

[120]  Hans Van de Vyver,et al.  On the generation of P-stable exponentially fitted Runge-Kutta-Nyström methods by exponentially fitted Runge-Kutta methods , 2006 .

[121]  Ch. Tsitouras,et al.  On Ninth Order, Explicit Numerov-Type Methods with Constant Coefficients , 2018 .

[122]  Theodore E. Simos,et al.  Exponentially Fitted Symplectic Runge-Kutta-Nystr om methods , 2013 .

[123]  Luis Rández,et al.  Two new embedded pairs of explicit Runge-Kutta methods adapted to the numerical solution of oscillatory problems , 2015, Appl. Math. Comput..

[124]  Ch. Tsitouras,et al.  Evolutionary Derivation of Sixth-Order P-stable SDIRKN Methods for the Solution of PDEs with the Method of Lines , 2019, Mediterranean Journal of Mathematics.

[125]  Beatrice Paternoster,et al.  A conditionally P-stable fourth-order exponential-fitting method for y '' = f ( f, y ) , 1999 .

[126]  Liviu Gr. Ixaru,et al.  Numerical Operations on Oscillatory Functions , 2001, Comput. Chem..

[127]  Wei Zhang,et al.  A High-Order Two-Step Phase-Fitted Method for the Numerical Solution of the Schrödinger Equation , 2016 .

[129]  M. M. Chawla,et al.  Numerov made explicit has better stability , 1984 .

[130]  Jesús Vigo-Aguiar,et al.  A Parallel Boundary Value Technique for Singularly Perturbed Two-Point Boundary Value Problems , 2004, The Journal of Supercomputing.

[131]  A. D. Raptis,et al.  A method for the solution of the Schrödinger equation , 1987 .

[132]  D. G. Bettis,et al.  Stabilization of Cowell's method , 1969 .

[133]  Theodore E. Simos,et al.  Phase-fitted Runge-Kutta pairs of orders 8(7) , 2017, J. Comput. Appl. Math..

[134]  Ch. Tsitouras,et al.  Trigonometric-Fitted Explicit Numerov-Type Method with Vanishing Phase-Lag and Its First and Second Derivatives , 2018, Mediterranean Journal of Mathematics.

[135]  M. M. Chawla,et al.  Families of fifth order Nyström methods for y″=f(x, y) and intervals of periodicity , 1981, Computing.

[136]  T. E. Simos,et al.  A multiple stage absolute in phase scheme for chemistry problems , 2019, Journal of Mathematical Chemistry.

[137]  Liviu Gr. Ixaru,et al.  Truncation Errors in Exponential Fitting for Oscillatory Problems , 2006, SIAM J. Numer. Anal..

[138]  M. Chawla.  Unconditionally stable noumerov-type methods for second order differential equations , 1983 .

[139]  M. Chawla,et al.  A two-stage fourth-order “almost” P-stable method for oscillatory problems , 1998 .

[140]  Theodore E. Simos,et al.  A new family of 7 stages, eighth-order explicit Numerov-type methods , 2017 .

[141]  Jesús Vigo-Aguiar,et al.  Adapted BDF Algorithms: Higher-order Methods and Their Stability , 2007, J. Sci. Comput..

[142]  Theodore E. Simos,et al.  New modified Runge-Kutta-Nyström methods for the numerical integration of the Schrödinger equation , 2010, Comput. Math. Appl..

[143]  A. Konguetsof.  A new two-step hybrid method for the numerical solution of the Schrödinger equation , 2010 .

[144]  T. Simos,et al.  Hybrid, phase–fitted, four–step methods of seventh order for solving x″(t) = f(t,x) , 2019, Mathematical Methods in the Applied Sciences.

[145]  M. Rizea,et al.  A numerov-like scheme for the numerical solution of the Schrödinger equation in the deep continuum spectrum of energies , 1980 .

[146]  T. E. Simos,et al.  A new two stage symmetric two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the radial Schrödinger equation , 2015, Journal of Mathematical Chemistry.

[147]  A. D. Raptis,et al.  Exponentially-fitted solutions of the eigenvalue Shrödinger equation with automatic error control , 1983 .

[148]  Manuel Calvo,et al.  Sixth-order symmetric and symplectic exponentially fitted modified Runge-Kutta methods of Gauss type , 2008, Comput. Phys. Commun..

[149]  T. E. Simos,et al.  An economical eighth-order method for the approximation of the solution of the Schrödinger equation , 2017, Journal of Mathematical Chemistry.

[150]  John P. Coleman,et al.  Mixed collocation methods for y ′′ =f x,y , 2000 .

[151]  A New Optimized Symmetric Embedded Predictor- Corrector Method (EPCM) for Initial-Value Problems with Oscillatory Solutions , 2014 .

[152]  M. van Daele,et al.  P-stable Obrechkoff methods of arbitrary order for second-order differential equations , 2007 .

[153]  Theodore E. Simos,et al.  Evolutionary generation of high‐order, explicit, two‐step methods for second‐order linear IVPs , 2017 .

[154]  T. Simos.  Exponentially and Trigonometrically Fitted Methods for the Solution of the Schrödinger Equation , 2010 .

[155]  J. M. Franco,et al.  Symplectic explicit methods of Runge-Kutta-Nyström type for solving perturbed oscillators , 2014, J. Comput. Appl. Math..

[156]  F. Iavernaro,et al.  High-order Symmetric Schemes for the Energy Conservation of Polynomial Hamiltonian Problems 1 2 , 2009 .

[157]  Guido Vanden Berghe,et al.  P-stable exponentially-fitted Obrechkoff methods of arbitrary order for second-order differential equations , 2007, Numerical Algorithms.

[158]  A. D. Raptis,et al.  Two-step methods for the numerical solution of the Schrödinger equation , 1982, Computing.

[159]  Luis Rández,et al.  Optimization of explicit two-step hybrid methods for solving orbital and oscillatory problems , 2014, Comput. Phys. Commun..

[160]  Manuel Calvo,et al.  Structure preservation of exponentially fitted Runge-Kutta methods , 2008 .

[161]  M. M. Chawla,et al.  Two-step fourth-order P-stable methods with phase-lag of order six for y ″=( t,y ) , 1986 .

[162]  Guido Vanden Berghe,et al.  Finite difference approach for the two-dimensional Schrödinger equation with application to scission-neutron emission , 2008, Comput. Phys. Commun..

[163]  T. E. Simos,et al.  A new multistep method with optimized characteristics for initial and/or boundary value problems , 2018, Journal of Mathematical Chemistry.

[164]  Manuel Calvo,et al.  On high order symmetric and symplectic trigonometrically fitted Runge-Kutta methods with an even number of stages , 2010 .

[165]  D. Hollevoet,et al.  The optimal exponentially-fitted Numerov method for solving two-point boundary value problems , 2009 .

[166]  Hans Van de Vyver,et al.  Comparison of some special optimized fourth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation , 2005, Comput. Phys. Commun..

[167]  Jesús Vigo-Aguiar,et al.  Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods , 2005, Math. Comput. Model..

[168]  A. C. Allison,et al.  The numerical solution of coupled differential equations arising from the Schrödinger equation , 1970 .

[169]  Theodore E. Simos,et al.  An eight-step semi-embedded predictor-corrector method for orbital problems and related IVPs with oscillatory solutions for which the frequency is unknown , 2015, J. Comput. Appl. Math..

[170]  T. E. Simos,et al.  Modified two‐step hybrid methods for the numerical integration of oscillatory problems , 2017 .

[171]  Xinyuan Wu,et al.  Note on derivation of order conditions for ARKN methods for perturbed oscillators , 2009, Comput. Phys. Commun..

[172]  Vladislav N. Kovalnogov,et al.  Modeling and Development of Cooling Technology of Turbine Engine Blades , 2015 .