New high order multiderivative explicit four-step methods with vanished phase-lag and its derivatives for the approximate solution of the Schrodinger equation. Part I: Construction and theoretical analysis

被引：67

作者：

Simos, T. E. ^{[1
,2
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia

[2] Univ Peloponnese, Fac Sci & Technol, Dept Comp Sci & Technol, Sci Computat Lab, Tripoli 22100, Greece

来源：

JOURNAL OF MATHEMATICAL CHEMISTRY | 2013年 / 51卷 / 01期

关键词：

Numerical solution; Schrodinger equation; Multistep methods; Multiderivative methods; Obrechkoff methods; Interval of periodicity; P-stability; Phase-lag; Phase-fitted; Derivatives of the phase-lag; TRIGONOMETRICALLY-FITTED FORMULAS; RUNGE-KUTTA METHODS; SYMMETRIC MULTISTEP METHODS; INITIAL-VALUE PROBLEMS; PREDICTOR-CORRECTOR METHODS; LONG-TIME INTEGRATION; NUMEROV-TYPE METHOD; NUMERICAL-SOLUTION; SYMPLECTIC METHODS; SPECIAL-ISSUE;

D O I：

10.1007/s10910-012-0074-y

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

In this paper we develop and study new high algebraic order multiderivative explicit four-step method with phase-lag and its first, second and third derivatives equal to zero. For the produced methods we investigate their errors and stability. Based on the above mentioned analysis we will arrive to some remarks and conclusions about their the efficiency to the numerical integration of the radial Schrodinger equation.

引用

页码：194 / 226

页数：33

共 114 条

[1] Symmetric multistep Obrechkoff methods with zero phase-lag for periodic initial value problems of second order differential equations
Achar, Sujatha D.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2011, 218 (05) : 2237 - 2248
[2] A new family of symmetric linear four-step methods for the efficient integration of the Schrodinger equation and related oscillatory problems
Alolyan, I.
Anastassi, Z. A.
Simos, T. E.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (09) : 5370 - 5382
[3] Alolyan I, J MATH CHEM IN PRESS
[4] A family of high-order multistep methods with vanished phase-lag and its derivatives for the numerical solution of the Schrodinger equation
Alolyan, Ibraheem
Simos, T. E.
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (10) : 3756 - 3774
[5] Alolyan I, 2011, MATCH-COMMUN MATH CO, V66, P473
[6] A family of ten-step methods with vanished phase-lag and its first derivative for the numerical solution of the Schrodinger equation
Alolyan, Ibraheem
Simos, T. E.
[J]. JOURNAL OF MATHEMATICAL CHEMISTRY, 2011, 49 (09) : 1843 - 1888
[7] A family of eight-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrodinger equation
Alolyan, Ibraheem
Simos, T. E.
[J]. JOURNAL OF MATHEMATICAL CHEMISTRY, 2011, 49 (03) : 711 - 764
[8] Mulitstep methods with vanished phase-lag and its first and second derivatives for the numerical integration of the Schrodinger equation
Alolyan, Ibraheem
Simos, T. E.
[J]. JOURNAL OF MATHEMATICAL CHEMISTRY, 2010, 48 (04) : 1092 - 1143
[9] High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrodinger equation
Alolyan, Ibraheem
Simos, T. E.
[J]. JOURNAL OF MATHEMATICAL CHEMISTRY, 2010, 48 (04) : 925 - 958
[10] A family of exponentially-fitted Runge-Kutta methods with exponential order up to three for the numerical solution of the Schrodinger equation
Anastassi, Z. A.
Simos, T. E.
[J]. JOURNAL OF MATHEMATICAL CHEMISTRY, 2007, 41 (01) : 79 - 100

← 1 2 3 4 5 6 7 8 9 10 →