Simulation of 2D and 3D inverse source problems of nonlinear time-fractional wave equation by the meshless homogenization function method

Abstract

In this paper, homogenization functions are first proposed to address two-dimensional (2D) and three-dimensional (3D) inverse source problems of nonlinear time-fractional wave equation (ISPs-NTFWE). Homogenization functions for 2D and 3D problems can be derived based on proposed conditions. Then, the superposition of homogenization function method (SHFM) for tackling ISPs-NTFWE is obtained. This new scheme can directly deal with 2D and 3D ISPs-NTFWEs via resolving a linear matrix system. Importantly, the proposed SHFM has the advantage of not involving mesh generation, numerical integration, iteration, regularization and fundamental solutions. In addition, it is easy to program and implement which can achieve accurate results even for 10% noisy boundary data. Several numerical examples have been assessed to verify the accuracy of the developed method for ISPs-NTFWE.