Mohamed Reda Ali Mohamed
Asst. Professor
Efficient computational approaches for fractional-order Degasperis-Procesi and Camassa–Holm equations
Results in Physics • 2023
Publication Information
Authors
Kezheng Zhang
a,1,2
, Azzh Saad Alshehry
b,2
, Noufe H. Aljahdaly
c,2
, Rasool Shah
d,2
,
Nehad Ali Shah
e,1,2
, Mohamed R. Ali
f,g,∗,2
Keywords
Aboodh transformation
Camassa–Holm and Degasperis–Procesi
equations
Series solution
Adomian decomposition method
Homotopy perturbation method
Journal
Results in Physics
Publisher
Not Available
Volume
Not Available
Issue
Not Available
Pages
Not Available
publication.type
International
Paper Link
Not Available
Supplementary Materials
Not Available
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.
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.