The use of local radial point interpolation method for solving two-dimensional linear fractional cable equation

An efficient numerical technique is formulated to solve two-dimensional time fractional cable equation. The fractional cable equation is an important mathematical model for describing anomalous diffusion processes in biological systems. The proposed computational technique is based on the combination of time stepping method and meshless weak formulation. At the first step, some implicit difference schemes are used to discrete the appearing integer and fractional time derivatives. Then, local radial point interpolation method (LRPI) is extended and used to solve the semi-discretized problem. The main aim of the paper is to show that the LRPI method is a powerful alternative computational technique to solve complicated fractional problems with high accuracy and low complexity. The performance and accuracy of the method are studied and verified through numerical experiments. Moreover, the convergence rate of the temporal discretization scheme is investigated numerically.