A composite numerical scheme for the numerical simulation of coupled Burgers' equation

In this work, a composite numerical scheme based on finite difference and Haar wavelets is proposed to solve time dependent coupled Burgers' equation with appropriate initial and boundary conditions. Time derivative is discretized by forward difference and then quasilinearization technique is used to linearize the coupled Burgers' equation. Space derivatives discretization with Haar wavelets leads to a system of linear equations and is solved using Matlab7.0. Convergence analysis of proposed scheme exhibits that the error bound is inversely proportional to the resolution level of the Haar wavelet. Finally, the adaptability of proposed scheme is demonstrated by numerical experiments and shows that the present composite scheme offers better accuracy in comparison with other existing numerical methods.