Numerical simulation of 3-D fractional-order convection-diffusion PDE by a local meshless method

Abstract

In this article, we present an efficient local meshless method for the numerical treatment of 3-D convection-diffusion PDE. The demand of meshless techniques increment because of its meshless nature and simplicity of usage in higher dimensions. This technique approximates the solution on set of uniform and scattered nodes. The space derivatives of the models are discretized by the proposed meshless procedure though the time fractional part is discretized by Liouville-Caputo fractional derivative. Some test problems on regular and irregular computational domains are presented to verify the validity, efficiency, and accuracy of the method.