Numerical solution of an inverse source problem for a time-fractional PDE via direct meshless local Petrov–Galerkin method

Abstract

In this paper, we employ an improved Meshless Local Petrov–Galerkin (MLPG), namely Direct Meshless Local Petrov–Galerkin (DMLPG) method, for solving an inverse time-dependent source problem for two-dimensional fractal mobile/immobile solute transport equation on regular and irregular domains. In the weak form DMLPG method, numerical integrations apply over low-degree polynomial basis functions instead of complicated moving least squares (MLS) shape functions of MLPG method. Therefore, the computational costs often reduce in the DMLPG method. In space domain, we employ the DMLPG method and the time derivatives of problem are discretized based on finite difference schemes. Numerical results demonstrate efficiency and accuracy of the proposed algorithm for solving the inverse source problem.