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.

本文提出了一种新颖的数值技术，可以准确有效地解决非线性时分波方程的反源问题。根据所有给定条件，可以推导非线性时间分数波方程的均化函数，然后得到一族均化函数。此外，通过均化函数的叠加建立了数值模型，并将其用于解决反源问题。所提出的方法没有网格生成，数值积分，迭代，正则化和基本解决方案，并且易于在现有软件上进行编程和实现。三个数值实验表明，即使在边界条件上施加了很大的噪声，所提出的逆源问题策略的准确性和收敛性。