Two-dimensional Haar Wavelet Method for Numerical Solution of Delay Partial Differential Equations

Abstract

In this paper, a two-dimensional Haar wavelet collocation method is applied to obtain the numerical solution of delay and neutral delay partial differential equations. Both linear and nonlinear problems can be solved using this method. Some benchmark test problems are given to verify the efficiency and accuracy of the aforesaid method. The results are compared with the exact solution and performance of the two-dimensional Haar collocation technique is measured by calculating the maximum absolute and root mean square errors for different numbers of grid points. The results are also compared with finite difference technique and one-dimensional Haar wavelet technique. The numerical results show that the two-dimensional Haar method is simply applicable, accurate and efficient.