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

Document Type

Journal Article

Publisher

Elsevier

Faculty

Faculty of Health, Engineering and Science

School

School of Engineering

RAS ID

18452

Comments

Mechee M., Ismail F., Hussain Z.M., Siri Z. (2014). Direct numerical methods for solving a class of third-order partial differential equations. Applied Mathematics and Computation, 247, 663-674. Available here

Abstract

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.

DOI

10.1016/j.amc.2014.09.021

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