Direct numerical methods for solving a class of third-order partial differential equations
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.
Keywords
Method of lines, ODEs, PDE, RKD method, System of, Third-order Differential equations, Finite difference method, Ordinary differential equations, Partial differential equations, Runge Kutta methods, Method of lines, ODEs, PDE, RKD method, System of, Third-order, Numerical methods
Document Type
Journal Article
Date of Publication
1-1-2014
Faculty
Faculty of Health, Engineering and Science
Publisher
Elsevier
School
School of Engineering
RAS ID
18452
Copyright
subscription content
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