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Direct numerical methods for solving a class of third-order partial differential equations.
- Source :
-
Applied Mathematics & Computation . Nov2014, Vol. 247, p663-674. 12p. - Publication Year :
- 2014
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00963003
- Volume :
- 247
- Database :
- Academic Search Index
- Journal :
- Applied Mathematics & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 99066554
- Full Text :
- https://doi.org/10.1016/j.amc.2014.09.021