A novel homogenization function method for inverse source problem of nonlinear time-fractional wave equation

Abstract

A novel numerical technique is developed in this paper to accurately and efficiently resolve the inverse source problem of the nonlinear time-fractional wave equation. Based on all given conditions, the homogenization function of nonlinear time-fractional wave equation can be derived, and then a family of homogenization functions is obtained. Furthermore, a numerical model is established by the superposition of homogenization functions and used for tackling inverse source problem. The proposed method is free of mesh generation, numerical integration, iteration, regularization and fundamental solutions, and it is easy to program and implement on the existing software. Three numerical experiments demonstrate the accuracy and convergence of the proposed strategy for the inverse source problem even with high noise imposed on the boundary conditions.