Solving Linear PDEs with the Aid of Two-Dimensional Legendre Wavelets

摘要

In this paper, we develop a method, which using two-dimensional Legendre wavelets, to solve linear PDEs. Based on the properties of shifted Legendre polynomials, we give a brief proof about the general procedure of two-dimensional operational matrices of integration, and then employ aforementioned matrices to find the solution of the PDEs. The proposed method is mathematically simple and fast. To demonstrate the efficiency of the method, two test problems (solution of the diffusion, Poisson) are discussed. The experimental results showed that the accuracy of the method is very high and only need a small number of collocation points.