Efficient computational approaches for fractional-order Degasperis-Procesi and Camassa–Holm equations

Abstract

In this study, we present a comprehensive comparison of two powerful analytical techniques, Aboodh Adomian decomposition method (AADM) and homotopy perturbation transform method (HPTM), for obtaining series solutions of nonlinear partial differential equations, specifically focusing on Camassa–Holm (CH) and Degasperis–Procesi (DP) equations. These equations are widely used to describe various nonlinear wave phenomena in fluid mechanics, optical fibers, and other applications. By applying both AADM and HPTM to CH and DP equations, we demonstrate the effectiveness and efficiency of each method in terms of accuracy, convergence, and computational complexity. Furthermore, we provide a detailed analysis of the series solutions obtained by each method and discuss their respective advantages and limitations. The results reveal that both methods are capable of providing accurate and convergent series solutions for the considered equations. However, AADM shows a slightly better performance in terms of convergence rate and ease of implementation, making it a preferable choice for solving CH and DP equations. This comparative study serves as a useful reference for researchers and practitioners working in the field of nonlinear partial differential equations and their applications.