A meshless localized collocation method for solving the two-dimensional inverse time fractional diffusion equation with nonlocal integral boundary condition

Inthispaper,thenumericalsolutionofthetwo-dimensionalinversetimefractionaldiffusionequationwithanonlocal boundary condition is investigated. It is obvious and well-known that in such problems, collocation methods based on the global basis function lead to the ill-conditioned coefficient matrices. To overcome this trouble, a meshless localized collocation method based on the local radial point interpolation method is proposed for solving this problem. In this procedure, general multiquadric radial basis function (GMQ-RBF) is used to construct shape functions. Also, an implicit finite difference method is employed to discrete the problem in time direction by approximating the appearing Caputo time fractional derivative. A numerical example demonstrates the efficiency and accuracy of the suggested method