High order closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the Schrödinger equation
暂无分享,去创建一个
[1] A. C. Allison,et al. Exponential-fitting methods for the numerical solution of the schrodinger equation , 1978 .
[2] Zacharias A. Anastassi,et al. A Family of Exponentially-fitted Runge–Kutta Methods with Exponential Order Up to Three for the Numerical Solution of the Schrödinger Equation , 2007 .
[3] Francesca Mazzia,et al. Hybrid Mesh Selection Algorithms Based on Conditioning for Two-Point Boundary Value Problems , 2006 .
[4] Theodore E. Simos,et al. A P-stable exponentially fitted method for the numerical integration of the Schrödinger equation , 2000, Appl. Math. Comput..
[5] T. E. Simos,et al. A two-step method for the numerical solution of the radial Schrödinger equation , 1995 .
[6] Stuart A. Rice,et al. New methods in computational quantum mechanics , 1996 .
[7] Tom E. Simos,et al. A Numerov-type method for the numerical solution of the radial Schro¨dinger equation , 1991 .
[8] J. Cash,et al. Variable Step Runge-Kutta-Nystrom Methods for the Numerical Solution of Reversible Systems , 2006 .
[9] Tom E. Simos,et al. A Modified Phase-Fitted Runge–Kutta Method for the Numerical Solution of the Schrödinger Equation , 2001 .
[10] G. Avdelas,et al. A Generator and an Optimized Generator of High-Order Hybrid Explicit Methods for the Numerical Solution of the Schrödinger Equation. Part 1. Development of the Basic Method , 2001 .
[11] Theodore E. Simos,et al. A Family of Numerov-type Exponentially Fitted Methods for the Numerical Integration of the Schrödinger Equation , 1997, Comput. Chem..
[12] T. E. Simos,et al. A Family of Trigonometrically-Fitted Symmetric Methods for the Efficient Solution of the Schrödinger Equation and Related Problems , 2003 .
[13] T. E. Simos. P-stable Four-Step Exponentially-Fitted Method for the Numerical Integration of the Schr¨odinger Equation , 2005 .
[14] Theodore E. Simos,et al. A Modified Runge-Kutta Method with Phase-lag of Order Infinity for the Numerical Solution of the Schrödinger Equation and Related Problems , 2001, Comput. Chem..
[15] T. E. Simos,et al. Family of Twelve Steps Exponential Fitting Symmetric Multistep Methods for the Numerical Solution of the Schrödinger Equation , 2002 .
[16] G. Avdelas,et al. Embedded eighth order methods for the numerical solution of the Schrödinger equation , 1999 .
[17] T. E. Simos,et al. Modified Runge-Kutta methods for the numerical solution of ODEs with oscillating solutions , 1997 .
[18] T. E. Simos,et al. A Family Of Numerov-Type Exponentially Fitted Predictor-Corrector Methods For The Numerical Integrat , 1996 .
[19] Theodore E. Simos,et al. On Finite Difference Methods for the Solution of the Schrödinger Equation , 1999, Comput. Chem..
[20] Theodore E. Simos,et al. Exponentially-fitted Runge-Kutta-Nystro"m method for the numerical solution of initial-value problems with oscillating solutions , 2002, Appl. Math. Lett..
[21] Zacharoula Kalogiratou,et al. Newton--Cotes formulae for long-time integration , 2003 .
[22] Donato Trigiante,et al. Discrete Conservative Vector Fields Induced by the Trapezoidal Method , 2006 .
[23] T. Simos,et al. On the Construction of Exponentially-Fitted Methods for the Numerical Solution of the Schrödinger Equation , 2001 .
[24] K. Tselios,et al. Symplectic Methods for the Numerical Solution of the Radial Shrödinger Equation , 2003 .
[25] T. E. Simos. AN EXPLICIT HIGH ORDER PREDICTOR-CORRECTOR METHOD FOR PERIODIC INITIAL VALUE PROBLEMS , 1995 .
[26] T. Simos,et al. Sixth algebraic order trigonometrically fitted predictor–corrector methods for the numerical solution of the radial Schrödinger equation , 2005 .
[27] Theodore E. Simos,et al. Explicit exponentially fitted methods for the numerical solution of the Schrödinger equation , 1999, Appl. Math. Comput..
[28] T. E. Simos. Some New Four-Step Exponential-Fitting Methods for the Numerical Solution of the Radical Schrödinger Equation , 1991 .
[30] Liviu Gr Ixaru,et al. Numerical methods for differential equations and applications , 1984 .
[31] Ch. Tsitouras,et al. High algebraic, high phase-lag order embedded Numerov-type methods for oscillatory problems , 2002, Appl. Math. Comput..
[32] Tom E. Simos. A New Numerov-Type Method For Computing Eigenvalues And Resonances Of The Radial Schrödinger Equation , 1996 .
[33] T. E. Simos,et al. Embedded methods for the numerical solution of the Schrödinger equation , 1996 .
[34] T. E. Simos,et al. A generator of high-order embedded P-stable methods for the numerical solution of the Schro¨dinger equation , 1996 .
[35] Theodore E. Simos,et al. Zero Dissipative, Explicit Numerov-Type Methods for Second Order IVPs with Oscillating Solutions , 2003, Numerical Algorithms.
[37] T. E. Simos,et al. Some new Numerov-type methods with minimal phase lag for the numerical integration of the radial Schrödinger equation , 1994 .
[38] G. Herzberg,et al. Spectra of diatomic molecules , 1950 .
[39] Zacharoula Kalogiratou,et al. Construction of Trigonometrically and Exponentially Fitted Runge–Kutta–Nyström Methods for the Numerical Solution of the Schrödinger Equation and Related Problems – a Method of 8th Algebraic Order , 2002 .
[40] Xiao-yan Liu,et al. Numerical solution of one‐dimensional time‐independent Schrödinger equation by using symplectic schemes , 2000 .
[41] Novriana Sumarti,et al. The Derivation of Interpolants for Nonlinear Two-Point Boundary Value Problems , 2006 .
[42] Xinsheng Zhao,et al. Numerical methods with a high order of accuracy applied in the quantum system , 1996 .
[43] T. E. Simos. Runge-Kutta interpolants with minimal phase-lag☆ , 1993 .
[44] D. P. Sakas,et al. A family of multiderivative methods for the numerical solution of the Schrödinger equation , 2005 .
[45] T. Simos,et al. The numerical solution of the radial Schrödinger equation via a trigonometrically fitted family of seventh algebraic order Predictor–Corrector methods , 2006 .
[46] A. Hinchliffe,et al. Chemical Modelling: Applications and Theory , 2008 .
[47] T. E. Simos,et al. A sixth-order exponentially fitted method for the numerical solution of the radial , 1990 .
[48] T. E. Simos,et al. New P-Stable Eighth Algebraic Order Exponentially-Fitted Methods for the Numerical Integration of the Schrödinger Equation , 2002 .
[49] J. W. Cooley,et al. An improved eigenvalue corrector formula for solving the Schrödinger equation for central fields , 1961 .
[50] J. M. Sanz-Serna,et al. Numerical Hamiltonian Problems , 1994 .
[51] Alessandra Sestini,et al. BS Linear Multistep Methods on Non-uniform Meshes , 2006 .
[52] Theodore E. Simos,et al. Numerical solution of the two-dimensional time independent Schrödinger equation with Numerov-type methods , 2005 .
[53] Zacharias A. Anastassi,et al. Trigonometrically fitted Runge–Kutta methods for the numerical solution of the Schrödinger equation , 2005 .
[54] T. Simos. An Eighth Order Exponentially Fitted Method for the Numerical Solution of the Schrödinger Equation , 1998 .
[55] T. E. Simos,et al. A four-step exponentially fitted method for the numerical solution of the Schrödinger equation , 2006 .
[56] David Moore,et al. On High Order MIRK Schemes and Hermite-Birkhoff Interpolants , 2006 .
[57] Theodore E. Simos,et al. Bessel and Neumann-fitted Methods for the Numerical Solution of the Radial Schrödinger Equation , 1997, Comput. Chem..
[58] T. E. Simos,et al. A family of P-stable exponentially‐fitted methods for the numerical solution of the Schrödinger equation , 1999 .
[59] T. E. Simos. Predictor-corrector phase-fitted methods for Y{double_prime} = F(X,Y) and an application to the Schroedinger equation , 1995 .
[60] M. M. Chawla,et al. Numerov made explicit has better stability , 1984 .
[61] T. E. Simos,et al. A Family of P-stable Eighth Algebraic Order Methods with Exponential Fitting Facilities , 2001 .
[62] T. E. Simos,et al. Eighth order methods with minimal phase‐lag for accurate computations for the elastic scattering phase‐shift problem , 1997 .
[63] A. Messiah. Quantum Mechanics , 1961 .
[64] Theodore E. Simos,et al. Explicit high order methods for the numerical integration of periodic initial-value problems , 1998, Appl. Math. Comput..
[65] G. Psihoyios. A Block Implicit Advanced Step-point (BIAS) Algorithm for Stiff Differential Systems , 2006 .
[66] T. E. Simos. A high order predictor-corrector method for periodic IVPS , 1993 .
[67] T. E. Simos,et al. Symmetric Eighth Algebraic Order Methods with Minimal Phase-Lag for the Numerical Solution of the Schrödinger Equation , 2002 .
[68] W. Enright. On the use of ‘arc length’ and ‘defect’ for mesh selection for differential equations , 2005 .
[69] T. Simos. EIGHTH-ORDER METHOD FOR ACCURATE COMPUTATIONS FOR THE ELASTIC SCATTERING PHASE-SHIFT PROBLEM , 1998 .
[70] John M. Blatt,et al. Practical points concerning the solution of the Schrödinger equation , 1967 .
[71] T. E. Simos,et al. A new method for the numerical solution of fourth-order BVP's with oscillating solutions , 1996 .
[72] Ben P. Sommeijer,et al. Explicit Runge-Kutta (-Nyström) methods with reduced phase errors for computing oscillating solutions , 1987 .
[73] A. D. Raptis,et al. A four-step phase-fitted method for the numerical integration of second order initial-value problems , 1991 .
[74] T. Simos. High Algebraic Order Methods with Minimal Phase-Lag for Accurate Solution of the Schrödinger Equation , 1998 .
[75] T. Simos. Runge-Kutta-Nyström interpolants for the numerical integration of special second-order periodic initial-value problems☆ , 1993 .
[76] T. E. Simos,et al. Exponentially - Fitted Multiderivative Methods for the Numerical Solution of the Schrödinger Equation , 2004 .
[77] M H Chawla,et al. A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value , 1986 .
[78] Shuen-De Wu,et al. Open Newton–Cotes differential methods as multilayer symplectic integrators , 1997 .
[79] Donato Trigiante,et al. Stability and Conditioning in Numerical Analysis , 2006 .
[80] CLOSED NEWTON–COTES TRIGONOMETRICALLY-FITTED FORMULAE FOR LONG-TIME INTEGRATION , 2003 .
[81] G. Avdelas,et al. Dissipative high phase-lag order numerov-type methods for the numerical solution of the Schrodinger equation , 2000 .
[82] Theodore E. Simos. High-order closed Newton-Cotes trigonometrically-fitted formulae for long-time integration of orbital problems , 2008, Comput. Phys. Commun..
[83] T. E. Simos,et al. A new hybrid imbedded variable-step procedure for the numerical integration of the Schrödinger equation , 1998 .
[84] Tom E. Simos. A fourth algebraic order exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation , 2001 .
[85] J. Lambert,et al. Symmetric Multistip Methods for Periodic Initial Value Problems , 1976 .
[86] John P. Coleman,et al. Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine , 1989 .
[87] Z. Kalogiratou,et al. Trigonometrically fitted and exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation , 2006 .
[88] K. Tselios,et al. Symplectic Methods of Fifth Order for the Numerical Solution of the Radial Shrödinger Equation , 2004 .
[89] An exponentially-fitted and trigonometrically-fitted method for the numerical solution of periodic initial-value problems☆ , 2003 .
[90] M. Rizea,et al. A numerov-like scheme for the numerical solution of the Schrödinger equation in the deep continuum spectrum of energies , 1980 .
[91] Tom E. Simos,et al. A family of four-step exponential fitted methods for the numerical integration of the radial Schrödinger equation , 1994 .
[92] An extended numerov-type method for the numerical solution of the Schrödinger equation , 1997 .
[93] Tom E. Simos. An explicit almost P-stable two-step method with phase-lag of order infinity for the numerical integration of second-order pacific initial-value problems , 1992 .
[94] Yanyun Qu,et al. A new implementation of EN method , 1999, Appl. Math. Comput..
[95] Tom E. Simos. A new variable-step method for the numerical integration of special second-order initial value problems and their application to the one-dimensional Schrödinger equation , 1993 .
[96] Donato Trigiante,et al. Stability Analysis of Linear Multistep Methods via Polynomial Type Variation 1 , 2007 .
[97] Tom E. Simos. Some new variable-step methods with minimal phase lag for the numerical integration of special second-order initial-value problem , 1994 .
[98] J. Dormand,et al. High order embedded Runge-Kutta formulae , 1981 .
[100] Lawrence F. Shampine,et al. A User-Friendly Fortran BVP Solver , 2006 .
[101] J. Dormand,et al. A family of embedded Runge-Kutta formulae , 1980 .
[102] G. Avdelas,et al. A Generator and an Optimized Generator of High-Order Hybrid Explicit Methods for the Numerical Solution of the Schrödinger Equation. Part 2. Development of the Generator, Optimization of the Generator and Numerical Results , 2001 .
[103] Theodore E. Simos,et al. A new finite difference scheme with minimal phase-lag for the numerical solution of the Schrödinger equation , 1999, Appl. Math. Comput..
[104] I. Gladwell,et al. Numerical Solution of General Bordered ABD Linear Systems by Cyclic Reduction , 2006 .
[105] P. Henrici. Discrete Variable Methods in Ordinary Differential Equations , 1962 .
[106] Zacharoula Kalogiratou,et al. Exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation , 2003 .
[107] Jeff Cash,et al. Lobatto-Obrechkoff Formulae for 2nd Order Two-Point Boundary Value Problems , 2006 .
[108] T. E. Simos,et al. Some embedded modified Runge-Kutta methods for the numerical solution of some specific Schrödinger equations , 1998 .
[109] Tom E. Simos,et al. A Runge-Kutta Fehlberg method with phase-lag of order infinity for initial-value problems with oscillating solution , 1993 .
[110] T. Simos. A new explicit Bessel and Neumann fitted eighth algebraic order method for the numerical solution of the Schrödinger equation , 2000 .