A New Explicit Singularly P-Stable Four-Step Method for the Numerical Solution of Second-Order IVPs

被引：18

作者：

Khalsaraei, Mohammad Mehdizadeh ^{[1
]}

Shokri, Ali ^{[1
]}

机构：

[1] Univ Maragheh, Fac Math Sci, Maragheh, Iran

来源：

IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY | 2020年 / 11卷 / 01期

关键词：

Explicit methods; Phase-lag; Ordinary differential equations; P-stable; Symmetric multistep methods; Singularly P-stability; VANISHED PHASE-LAG; RADIAL SCHRODINGER-EQUATION; OBRECHKOFF METHOD; MULTISTEP METHODS; 4TH DERIVATIVES; 2-STEP METHOD; ORDER; INTEGRATION; FAMILY; 3RD;

D O I：

10.22052/ijmc.2020.207671.1472

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

In this paper, we introduce a new symmetric explicit four-step method with variable coefficients for the numerical solution of second-order linear periodic and oscillatory initial value problems of ordinary differential equations. For the first time in the literature, we generate an explicit method with the most important singularly P-stability property. The method is multiderivative and has algebraic order eight and infinite order of phase-lag. The numerical results for some chemical (e.g. orbit problems of Stiefel and Bettis) as well as quantum chemistry problems (i.e. systems of coupled differential equations) indicated that the new method is superior, efficient, accurate and stable. (C) 2020 University of Kashan Press. All rights reserved

引用

页码：17 / 31

页数：15

共 36 条

[1] Allison A. C., 1970, Journal of Computational Physics, V6, P378, DOI 10.1016/0021-9991(70)90037-9
[2] Dormand J.R., 1980, J COMPUT APPL MATH, V6, P19, DOI DOI 10.1016/0771-050X(80)90013-3
[3] HIGH-ORDER P-STABLE MULTISTEP METHODS
FRANCO, JM
PALACIOS, M
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1990, 30 (01) : 1 - 10
[4] A new family of two stage symmetric two-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrodinger equation
Hui, Fei
Simos, T. E.
[J]. JOURNAL OF MATHEMATICAL CHEMISTRY, 2015, 53 (10) : 2191 - 2213
[5] An explicit six-step singularly P-stable Obrechkoff method for the numerical solution of second-order oscillatory initial value problems
Khalsaraei, Mohammad Mehdizadeh
Shokri, Ali
[J]. NUMERICAL ALGORITHMS, 2020, 84 (03) : 871 - 886
[6] The New High Approximation of Stiff Systems of First Order IVPs Arising From Chemical Reactions by k-Step L-Stable Hybrid Methods
Khalsaraei, Mohammad Mehdizadeh
Shokri, Ali
Molayi, Maryam
[J]. IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, 2019, 10 (02): : 181 - 193
[7] LAMBERT JD, 1976, J I MATH APPL, V18, P189
[8] A two-step explicit P-stable method of high phase-lag order for second order IVPs
Li, QH
Wu, XY
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2004, 151 (01) : 17 - 26
[9] A two-step explicit P-stable method for solving second order initial value problems
Li, QH
Wu, XY
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2003, 138 (2-3) : 435 - 442
[10] A two-step explicit P-stable method of high phase-lag order for linear periodic IVPs
Li, Qinghong
Wu, Xinyuan
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 200 (01) : 287 - 296

← 1 2 3 4 →