A family of trigonometrically fitted partitioned Runge-Kutta symplectic methods

被引：147

作者：

Monovasilis, Th. ^{[1
]}

Kalogiratou, Z. ^{[2
]}

Simos, T. E. ^{[3
]}

机构：

[1] Technol Educ Inst Western Macedonia Kastoria, Dept Int Trade, Kastoria 52100, Greece

[2] Technol Educ Inst Western Macedonia Kastoria, Dept Informat & Comp Technol, Kastoria 52100, Greece

[3] Univ Peloponnese, Sci Computat Lab, Dept Comp Sci & Technol, Fac Sci & Technol, GR-22100 Tripolis, Greece

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 209卷 / 01期

关键词：

Trigonometrically fitted; Symplectic methods; Eigenvalue problem; Schrodinger equation; Shooting method; INITIAL-VALUE PROBLEMS; RADIAL SCHRODINGER-EQUATION; MINIMAL PHASE-LAG; PREDICTOR-CORRECTOR METHODS; FINITE-DIFFERENCE METHOD; NUMERICAL-SOLUTION; OSCILLATING SOLUTIONS; ORDER INFINITY; 2-STEP METHOD; INTEGRATION;

D O I：

10.1016/j.amc.2008.06.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are presenting a family of trigonometrically fitted partitioned Runge-Kutta symplectic methods of fourth order with six stages. The solution of the one-dimensional time independent Schrodinger equation is considered by trigonometrically fitted symplectic integrators. The Schrodinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator and the exponential potential. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：91 / 96

页数：6

共 49 条

[1] An optimized Runge-Kutta method for the solution of orbital problems [J].

Anastassi, ZA ;

Simos, TE .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 175 (01) :1-9

[2] Embedded methods for the numerical solution of the Schrodinger equation [J].

Avdelas, G ;

Simos, TE .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1996, 31 (02) :85-102

[3] A generator of high-order embedded P-stable methods for the numerical solution of the Schrodinger equation [J].

Avdelas, G ;

Simos, TE .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1996, 72 (02) :345-358

[4] Block Runge-Kutta methods for periodic initial-value problems [J].

Avdelas, G ;

Simos, TE .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1996, 31 (01) :69-83

[5] 4TH-ORDER SYMPLECTIC INTEGRATION [J].

FOREST, E ;

RUTH, RD .

PHYSICA D, 1990, 43 (01) :105-117

[6] A P-stable exponentially fitted method for the numerical integration of the Schrodinger equation [J].

Kalogiratou, Z ;

Simos, TE .

APPLIED MATHEMATICS AND COMPUTATION, 2000, 112 (01) :99-112

[7] Symplectic integrators for the numerical solution of the Schrodinger equation [J].

Kalogiratou, Z ;

Monovasilis, T ;

Simos, TE .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 158 (01) :83-92

[8] A generator of hybrid symmetric four-step methods for the numerical solution of the Schrodinger equation [J].

Konguetsof, A ;

Simos, TE .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 158 (01) :93-106

[9] An exponentially-fitted and trigonometrically-fitted method for the numerical solution of periodic initial-value problems [J].

Konguetsof, A ;

Simos, TE .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2003, 45 (1-3) :547-554

[10] THE ACCURACY OF SYMPLECTIC INTEGRATORS [J].

MCLACHLAN, RI ;

ATELA, P .

NONLINEARITY, 1992, 5 (02) :541-562

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