Jñānābha‎, Vol. 49 (1) (2019), 26-39

NUMERICAL SOLUTION OF THE CONVECTION DIFFUSION EQUATION BY THE LEGENDRE WAVELET METHOD

Devendra Chouhan
Dept. of Mathematics, IES, IPS Academy, Indore, India
Email:dchouhan100@gmail.com

R.S. Chandel
Govt. Geetanjali Girls College, Bhopal, India
Email:rs chandel2009@yahoo.co.in
(Received : January 08, 2019 ; Revised: June 03, 2019)



Abstract

In this paper, a numerical method is proposed for solving Convection Diffusion equations. The method is based upon the Legendre wavelet expansion. The Legendre wavelets operational matrix of integration is derived and utilized to transform the equation to a system of algebraic equations by combining collocation method. The proposed method is very convenient for solving such problems since conditions are taken into account automatically. Illustrative examples are included to demonstrate the validity and applicability of the proposed Legendre wavelets method. 

2010 Mathematics Subject Classifications: 42C40, 35A08, 65L60.
Keywords and phrases: Two - dimensional Legendre wavelets, Operational matrix of integration, Partial differential equations, Convection diffusion equation, Collocation method.