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.

在本文中，首先提出了均匀化函数来解决非线性时间分数波动方程 (ISPs-NTFWE) 的二维 (2D) 和三维 (3D) 逆源问题。2D 和 3D 问题的同质化函数可以根据建议的条件推导出来。然后，得到了解决ISPs-NTFWE的均质化函数叠加法（SHFM）。这种新方案可以通过解析线性矩阵系统直接处理 2D 和 3D ISPs-NTFWEs。重要的是，所提出的 SHFM 具有不涉及网格生成、数值积分、迭代、正则化和基本解决方案的优点。此外，它易于编程和实现，即使对于 10% 噪声边界数据也能获得准确的结果。