  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.
