Direct numerical methods for solving a class of third-order partial differential equations

被引：8

作者：

Mechee, M. ^{[1
,2
]}

Ismail, F. ^{[3
,4
]}

Hussain, Z. M. ^{[1
,5
]}

Siri, Z. ^{[2
]}

机构：

[1] Univ Kufa, Fac Math & Comp Sci, Najaf, Iraq

[2] Univ Malaya, Inst Math Sci, Kuala Lumpur 50603, Malaysia

[3] Univ Putra Malaysia, Dept Math, Upm Serdang 43400, Selangor, Malaysia

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

[5] Edith Cowan Univ, Sch Engn, Joondalup, WA 6027, Australia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 247卷

关键词：

RKD method; Method of lines; Third-order; PDE; System of ODEs; RUNGE-KUTTA TYPE; LINES;

D O I：

10.1016/j.amc.2014.09.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, three types of third-order partial differential equations (PDEs) are classified to be third-order PDE of type I, II and III. These classes of third-order PDEs usually occur in many subfields of physics and engineering, for example, PDE of type I occurs in the impulsive motion of a flat plate. An efficient numerical method is proposed for PDE of type I. The PDE of type I is converted to a system of third-order ordinary differential equations (ODEs) using the method of lines. The system of ODEs is then solved using direct Runge-Kutta which we derived purposely for solving special third-order ODEs of the form y ''' = f (x, y). Simulation results showed that the proposed RKD-based method is more accurate than the existing finite difference method. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：663 / 674

页数：12

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