An analysis of convergence of hybridized approximation techniques for the analytical solution of partial differential equations

Abstract

In this paper, we use the hybridization of two well-known semi-analytical methods to obtain the numerical solutions for some special linear and nonlinear partial differential equations that are predominant in most physical science disciplines. The first among these methods is the coupling of Laplace transform and Adomian decomposition method (LADM) while the second method is standard Homotopy perturbation method with Laplace transform method (HPTM). The accuracy and dependability of these proposed techniques is confirmed by applying them to solve linear and nonlinear Kleidon-Gordon equations, linear transverse equation of a vibrating beam, homogeneous and inhomogeneous nonlinear PDEs, advection equation, diffusion-convection and Korteweg-DeVries equation. Thereafter, comparison between the solutions obtained by the methods is presented in tables for convergence analysis. Consequently, the findings from our study showed the two methods can be effective alternative approaches for obtaining solutions to linear and nonlinear PDEs and higher-order initial value problems.