A meshless computational approach for solving two-dimensional inverse time-fractional diffusion problem with non-local boundary condition

Abstract

This paper is devoted to investigating a two-dimensional inverse anomalous diffusion problem. The missing solely time-dependent Dirichlet boundary condition is recovered by imposing an additional integral measurement over the domain. An efficient computational technique based on a combination of a time integration scheme and local meshless Petrov–Galerkin method is implemented to solve the governing inverse problem. Firstly, an implicit time integration scheme is used to discretize the model in the temporal direction. To fully discretize the model, the primary spatial domain is represented by a set of distributed nodes and data-dependent basis functions are constructed by using the radial point interpolation method. Then, the local meshless Petrov–Galerkin method is used to discretize the problem in the spatial direction. Numerical examples are presented to verify the accuracy and efficiency of the proposed technique. The stability of the method is examined when the input data are contaminated with noise.