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.
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页码：194 / 226
页数：33
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