An efficient and computational effective method for second order problems

被引：49
作者：
Ma, Jing [1 ]
Simos, T. E. [2 ,3 ]
机构：
[1] Changan Univ, Sch Informat Engn, Xian 710064, Shaanxi, Peoples R China
[2] Univ Peloponnese, Fac Econ Management & Informat, Dept Informat & Telecommun, Lab Computat Sci, Tripoli 22100, Greece
[3] 10 Konitsis St, Athens 17564, Greece
来源：
JOURNAL OF MATHEMATICAL CHEMISTRY | 2017年 / 55卷 / 08期
关键词：
Phase-lag; Derivative of the phase-lag; Initial value problems; Oscillating solution; Symmetric; Hybrid; Multistep; Schrodinger equation; VANISHED PHASE-LAG; INITIAL-VALUE-PROBLEMS; RADIAL SCHRODINGER-EQUATION; PREDICTOR-CORRECTOR METHOD; SYMMETRIC 2-STEP METHOD; EXPLICIT 4-STEP METHOD; P-STABLE METHOD; TRIGONOMETRICALLY-FITTED FORMULAS; KUTTA-NYSTROM METHODS; NUMERICAL-SOLUTION;
D O I：
10.1007/s10910-017-0753-9
中图分类号：
O6 [化学];
学科分类号：
0703 ;
摘要：
An efficient and computational effective algorithm is introduced, for the first time in the literature, in the present paper. The main properties of the scheme are: (1) the algorithm is a two-step scheme, (2) the algorithm is symmetric one, (3) it is a hight algebraic order scheme (i.e of eight algebraic order), (4) it is a three-stages algorithm, (5) the first layer of the new method is based on an approximation to the point , (6) the scheme has vanished phase-lag and its first, second and third derivatives, (7) the new proposed algorithm has an interval of periodicity equal to . For the present new scheme we study: (1) its construction, (2) its error analysis (3) its stability analysis. Finally, the investigation of the effectiveness of the new algorithm leads to its application to systems of differential equations arising from the Schrodinger equation.
引用
收藏
页码：1649 / 1668
页数：20
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