Construction of an optimized explicit Runge-Kutta-Nystrom method for the numerical solution of oscillatory initial value problems

被引：161

作者：

Kosti, A. A. ^{[1
]}

Anastassi, Z. A. ^{[2
]}

Simos, T. E. ^{[1
,3
]}

机构：

[1] Univ Peloponnese, Comp Sci Lab, Dept Comp Sci & Technol, Fac Sci & Technol, GR-22100 Tripolis, Greece

[2] Sch Pedag & Technol Educ ASPETE, Dept Sci, GR-14121 Athens, Greece

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

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 61卷 / 11期

关键词：

Numerical solution; Initial value problems; Explicit methods; Runge-Kutta-Nystrom methods; Phase-lag; Amplification factor;

D O I：

10.1016/j.camwa.2011.04.046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An explicit optimized Runge-Kutta-Nystrom method with four stages and fifth algebraic order is developed. The produced method has variable coefficients with zero phase-lag, zero amplification factor and zero first derivative of the amplification factor. We provide an analysis of the local truncation error of the new method. We also measure the efficiency of the new method in comparison to other numerical methods through the integration of the two-body problem with various eccentricities and three other periodical/oscillatory initial value problems. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：3381 / 3390

页数：10

共 21 条

[1]

ACETO L, 2008, J NUMER ANAL IND APP, V3, P181

[2]

An RT., 2008, J NUMERICAL ANAL IND, V2008

[3]

[Anonymous], 1967, J. Comput. Phys, DOI DOI 10.1016/0021-9991(67)90046-0

[4]

[Anonymous], SPECIALIST PERIODICA

[5]

[Anonymous], 2008, NUMER ANAL IND APPL

[6]

Chatterjee S., 2008, J NUMERICAL ANAL IND, V3, P193

[7]

Cooley J. W., 1961, MATH COMPUT, V15, P63

[8]

Dagnino C., 2008, J NUMERICAL ANAL IND, V3, P211

[9] FAMILIES OF RUNGE-KUTTA-NYSTROM FORMULAS [J].

DORMAND, JR ;

ELMIKKAWY, MEA ;

PRINCE, PJ .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1987, 7 (02) :235-250

[10]

Enachescu C., 2008, JNAIAM J NUMERICAL A, V3, P221

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