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

Hamid Mesgarani^{1},
Masoud Bakhshandeh^{1}, and Yones Esmaeelzade Aghdam^{*1}

^{1} Faculty of Science, Shahid Rajaee
Teacher Training University, Lavizan, Tehran, 16785-163

**Original:** 21 February 2020 **Revised:** 17 August 2020 **Accepted:** 26 September 2020 **Published online:** 20 December 2020

**Doi Link:**

**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.

**Key Words:**

*The partial differential equation, The two-dimensional Chebyshev wavelet, The theory of fractional derivatives, The convergence and error bound*