Numerical investigation of the two– dimensional time–dependent diffusion equation using Radial basis functions

Abstract

This paper develops a numerical method for solving the partial differential equation in terms of Caputo derivatives with Dirichlet boundary conditions. The approach is based on the two-dimensional Chebyshev wavelet of the second kind with the operational matrix of the collocation method. Furthermore, the convergence and error bound of the proposed method are investigated. For the illustration of the effects of the proposed method, we solve four examples by the presented technique. The obtained results are compared with the results obtained via other numerical methods in which our results are much more accurate than others.