Direct Integrators for the General Third-Order Ordinary Differential Equations with an Application to the Korteweg–de Vries Equation

被引：0

作者：

Jator S. ^{[1
]}

Okunlola T. ^{[2
]}

Biala T. ^{[3
]}

Adeniyi R. ^{[4
]}

机构：

[1] Department of Mathematics and Statistics, Austin Peay State University, Clarksville, 37044, TN

[2] Department of Physical and Mathematical Science, Afe Babalola University, P.M.B 5454, Ado Ekiti, Ekiti

[3] Department of Mathematics and Computer Science, Jigawa State University, P.M.B 048, Kafin Hausa

[4] Department of Mathematics, University of Ilorin, P.M.B 1515, Ilorin

来源：

International Journal of Applied and Computational Mathematics | 2018年 / 4卷 / 5期

关键词：

Boundary value methods; Convergence; Korteweg–de Vries equation; Linear multistep methods; Third order problems;

D O I：

10.1007/s40819-018-0542-6

中图分类号：

学科分类号：

摘要：

We construct a new class of implicit continuous linear multistep methods (LMMs) which are used as boundary value methods for the numerical integration of the general third order initial and boundary value problems in ordinary differential equations, including the Korteweg–de Vries equation. The boundary value methods obtained from these continuous LMMs are weighted the same and are used to simultaneously generate approximate solutions to the exact solutions in the entire interval of integration. We established the convergence analysis of the methods and several numerical examples are given to show the performance of the methods. © 2018, Springer Nature India Private Limited.

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