A note on homotopy perturbation approach for nonlinear coagulation equation to improve series solutions for longer times

Abstract

Abstract In this work, the approach presented in a recent publication by Kaur et al. (2019) is improved. The truncated series solution derived from the existing Homotopy Perturbation method (HPM) behaves peculiarly for a longer time domain and provides accurate results only for a shorter time. The Homotopy perturbation approach and the Pade approximation are coupled to estimate the nonlinear coagulation equation to tackle this problem. This significantly improves solution quality over a longer time frame by consuming fewer terms of the truncated series. The effectiveness of the new approach is tested by deriving the new analytical solutions of the number density function for a bilinear kernel with exponential initial distributions. In addition, the new solutions for physical relevant shear, Ruckenstein/Pulvermacher and Brownian kernels corresponding to exponential and gamma initial distributions are also derived. Due to the non-availability of the analytical solutions, the verification of the new results is done against the mass conserving finite volume scheme (Singh et al., 2015) for shear stress, bilinear and Brownian kernels.