Error analysis of modified Runge-Kutta-Nystrom methods for nonlinear second-order delay boundary value problems

被引：0

作者：

Zhang, Chengjian ^{[1
,2
]}

Wang, Siyi ^{[1
]}

Tang, Changyang ^{[1
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[2] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2023年 / 142卷

关键词：

Second-order boundary value; problems; Time-variable delay; Modified Runge-Kutta-Nystr?m; methods; Error analysis; DIFFERENTIAL-EQUATIONS; D-CONVERGENCE; STABILITY;

D O I：

10.1016/j.aml.2023.108658

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the numerical solutions of nonlinear second-order boundary value problems with time-variable delay. By adapting Runge-Kutta- Nystrom (RKN) methods and combining Lagrange interpolation, a class of modified RKN (MRKN) methods are suggested for solving the problems. Under some suitable conditions, MRKN methods are proved to be convergent of order min{p, q}, where p, q are the local orders of MRKN methods and Lagrange interpolation, respectively. Numerical experiments further confirm the computational effectiveness and accuracy of MRKN methods.(c) 2023 Elsevier Ltd. All rights reserved.

引用

页数：7

共 12 条

[1] A COLLOCATION METHOD FOR BOUNDARY-VALUE-PROBLEMS OF DIFFERENTIAL-EQUATIONS WITH FUNCTIONAL ARGUMENTS [J].

BELLEN, A ;

ZENNARO, M .

COMPUTING, 1984, 32 (04) :307-318

[2] NUMERICAL-METHOD TO BOUNDARY-VALUE PROBLEMS FOR 2ND ORDER DELAY DIFFERENTIAL-EQUATIONS [J].

CHOCHOLATY, P ;

SLAHOR, L .

NUMERISCHE MATHEMATIK, 1979, 33 (01) :69-75

[3]

Hairer E., 1987, Solving ordinary differential equations I. nonstiffproblems, DOI DOI 10.1016/0378-4754(87)90083-8

[4]

Henderson J., 1995, Boundary value problems for functional differential equations

[5]

Huang CM, 2001, J COMPUT MATH, V19, P259

[6] Stability analysis of Runge-Kutta methods for systems of delay differential equations [J].

intHout, KJ .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1997, 17 (01) :17-27

[7] Monotone method for second-order delayed differential equations with boundary value conditions [J].

Jankowski, T .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 149 (02) :589-598

[8]

Kolmanovskii V., 1999, Introduction to the Theory and Applications of Functional Differential Equations

[9] The extended generalized Stormer-Cowell methods for second-order delay boundary value problems [J].

Li, Cui ;

Zhang, Chengjian .

APPLIED MATHEMATICS AND COMPUTATION, 2017, 294 :87-95

[10] A subdivision approach to the construction of approximate solutions of boundary-value problems with deviating arguments [J].

Qu, R ;

Agarwal, RP .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1998, 35 (11) :121-135

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