A Class of Hybrid Methods for Direct Integration of Fourth-Order Ordinary Differential Equations

被引：2

作者：

Jikantoro, Y. D. ^{[1
,3
]}

Ismail, F. ^{[1
,2
]}

Senu, N. ^{[1
,2
]}

Ibrahim, Z. B. ^{[1
,2
]}

机构：

[1] Univ Putra Malaysia, Dept Math, Serdang 43400, Selangor, Malaysia

[2] Univ Putra Malaysia, Inst Math Res, Serdang 43400, Selangor, Malaysia

[3] Ibrahim Badamasi Babangida Univ, Dept Math, PMB 11, Lapai, Nigeria

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2018年 / 41卷 / 02期

关键词：

Hybrid method; Four-step method; B4-series; Order conditions; Fourth-order ordinary differential equations; INITIAL-VALUE PROBLEMS; RUNGE-KUTTA TYPE;

D O I：

10.1007/s40840-017-0520-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A class of hybrid methods for solving fourth-order ordinary differential equations (HMFD) is proposed and investigated. Using the theory of B-series, we study the order of convergence of the HMFD methods. The main result is a set of order conditions, analogous to those for two-step hybrid method, which offers a better alternative to the usual ad hoc Taylor expansions. Based on the algebraic order conditions, a one-stage and two-stage explicit HMFD methods are constructed. Results from numerical experiment suggest the superiority of the new methods in terms of accuracy and computational efficiency over hybrid methods for special second ODEs, Runge-Kutta methods recently proposed for solving special fourth-order ODEs directly and some linear multistep methods proposed for the same purpose in the literature.

引用

页码：985 / 1010

页数：26

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