Homotopy perturbation and adomian decomposition methods for condensing coagulation and Lifshitz-Slyzov models

Abstract

This article presents analytic approximate solutions of the condensing coagulation model (CCM) and Lifshitz-Slyzov equation (LSE) using two different semi-analytical schemes, namely the homotopy perturbation and Adomian decomposition methods. It is shown mathematically that the series solutions obtained using these techniques converge to the same set of solutions and therefore, justified the method’s reliability. Interestingly, for the CCM, scheme provides closed form solutions for the constant and product kernels. However, finite term approximated solutions are given for sum and Ruckenstein kernels which are physically relevant. Proceeding further, the truncated series solutions are discussed for LSE with constant kernel. To see the novelty of our proposed methods, numerical findings for number density and zeroth moment are compared to the exact solutions with given initial conditions and the errors between the approximated results are shown graphically.