The wavelet methods to linear and nonlinear reaction–diffusion model arising in mathematical chemistry

Abstract

In this paper, we have applied an accurate and efficient wavelet scheme (due to Legendre polynomial) to find the numerical solutions for a set of coupled reaction–diffusion equations. This technique provides the solutions in rapid convergence series with computable terms for the problems with high degree of non linear terms appearing in the governing differential equations. The highest derivative in the differential equation is expanded into wavelet series, this approximation is then integrated while the boundary conditions are applied by using integration constants. With the help of operational matrices, the nonlinear reaction–diffusion equations are converted into a system of algebraic equations. Finally, some numerical examples to demonstrate the validity and applicability of the method have been furnished. The use of Legendre wavelets is found to be accurate, efficient, simple, and computationally attractive. This wavelet method can be used for obtaining quick solution in many chemical Engineering problems.