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Z. Naturforsch. 67a, 267 – 274
(2012)
doi:10.5560/ZNA.2012-0026
Solution of the Coupled Burgers Equation Based on Operational Matrices of d-Dimensional Orthogonal Functions
1 Department of Mathematics, Imam Khomeini International University, Ghazvin 34149-16818, Iran
2 Department of Physics, Shahid Beheshti University, Evin, Tehran 19839, Iran
3 Department of Computer Sciences, Shahid Beheshti University, Evin, Tehran 19839, Iran
Received October 7, 2011 / published online May 2, 2012
Reprint requests to: S. K.; E-mail:
saeedkazem@gmail.com
This paper aims to construct a general formulation for the d-dimensional orthogonal functions and their derivative and product matrices. These matrices together with the Tau method are utilized to reduce the solution of partial differential equations (PDEs) to the solution of a system of algebraic equations. The proposed method is applied to solve homogeneous and inhomogeneous two-dimensional parabolic equations. Also, the mentioned method is employed to find the solution of the coupled Burgers equation. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.
Key words: Coupled Burgers Equation; Operational Matrix; Chebyshev and Legendre Polynomials; Tau Method.
Mathematics Subject Classification 2000: 34A08