The non-linear collision-induced breakage equation has significant applications in particulate processes. Two semi-analytical techniques, namely homotopy analysis method (HAM) and accelerated homotopy perturbation method (AHPM) are investigated along with the well-known finite volume method (FVM) to comprehend the dynamical behavior of the non-linear system, i.e., the concentration function, the total number and the total mass of the particles in the system. The theoretical convergence analyses of the series solutions of HAM and AHPM are discussed. In addition, the error estimations of the truncated solutions of both methods equip the maximum absolute error bound. To justify the applicability and accuracy of these methods, numerical simulations are compared with the findings of FVM and analytical solutions considering three physical problems.

翻译：非线性碰撞诱导破碎方程在颗粒过程中具有重要应用。本研究探讨了两种半解析技术——同伦分析法（HAM）与加速同伦摄动法（AHPM），并结合著名的有限体积法（FVM），以深入理解该非线性系统的动力学行为，即系统中的浓度函数、颗粒总数及总质量。讨论了HAM和AHPM级数解的理论收敛性分析。此外，两种方法截断解的误差估计提供了最大绝对误差界。为验证这些方法的适用性与准确性，将数值模拟结果与FVM及考虑三个物理问题的解析解进行了对比分析。