An economical eighth-order method for the approximation of the solution of the Schrodinger equation

被引：79
|
作者：
Wang, Zhiwei [1 ,2 ]
Simos, T. E. [3 ,4 ,5 ]
机构：
[1] Changan Univ, Sch Informat Engn, Xian 710064, Peoples R China
[2] Heilongjiang Transportat Informat & Telecommun Ct, Harbin 150081, Heilongjiang, Peoples R China
[3] Ural Fed Univ, Grp Modern Computat Methods, 19 Mira St, Ekaterinburg 620002, Russia
[4] Univ Peloponnese, Fac Econ Management & Informat, Dept Informat & Telecommun, Sci Computat Lab, Tripolis 22100, Greece
[5] 10 Konitsis St, Athens 17564, Greece
来源：
JOURNAL OF MATHEMATICAL CHEMISTRY | 2017年 / 55卷 / 03期
关键词：
Phase-lag; Derivative of the phase-lag; Symmetric; Multistep; Schrodinger equation; VANISHED PHASE-LAG; INITIAL-VALUE-PROBLEMS; PREDICTOR-CORRECTOR METHOD; SYMMETRIC 2-STEP METHOD; EXPLICIT 4-STEP METHODS; KUTTA-NYSTROM METHODS; P-STABLE METHOD; NUMERICAL-SOLUTION; MULTISTEP METHODS; 2ND DERIVATIVES;
D O I：
10.1007/s10910-016-0718-4
中图分类号：
O6 [化学];
学科分类号：
0703 ;
摘要：
In this paper we introduce, for the first time in the literature, a three-stages two-step method. The new algorithm has the following characteristics: (1) it is a two-step algorithm, (2) it is a symmetric method, (3) it is an eight-algebraic order method (i.e of high algebraic order), (4) it is a three-stages method, (5) the approximation of its first layer is done on the point and not on the usual point , (6) it has eliminated the phase-lag and its derivatives up to order two, (7) it has good stability properties (i.e. interval of periodicity equal to . For this method we present a detailed analysis : development, errorand stability analysis. The new proposed algorithm is applied to systems of differential equations of the Schrodinger type in order to examine its efficiency.
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页码：717 / 733
页数：17
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