On the Numerical Solution of 1D and 2D KdV Equations Using Variational Homotopy Perturbation and Finite Difference Methods

Abey Sherif Kelil () and Appanah Rao Appadu
Additional contact information
Abey Sherif Kelil: Department of Mathematics and Applied Mathematics, Nelson Mandela University, Port Elizabeth 6031, South Africa
Appanah Rao Appadu: Department of Mathematics and Applied Mathematics, Nelson Mandela University, Port Elizabeth 6031, South Africa

Mathematics, 2022, vol. 10, issue 23, 1-36

Abstract: The KdV equation has special significance as it describes various physical phenomena. In this paper, we use two methods, namely, a variational homotopy perturbation method and a classical finite-difference method, to solve 1D and 2D KdV equations with homogeneous and non-homogeneous source terms by considering five numerical experiments with initial and boundary conditions. The variational homotopy perturbation method is a semi-analytic technique for handling linear as well as non-linear problems. We derive classical finite difference methods to solve the five numerical experiments. We compare the performance of the two classes of methods for these numerical experiments by computing absolute and relative errors at some spatial nodes for short, medium and long time propagation. The logarithm of maximum error vs. time from the numerical methods is also obtained for the experiments undertaken. The stability and consistency of the finite difference scheme is obtained. To the best of our knowledge, a comparison between the variational homotopy perturbation method and the classical finite difference method to solve these five numerical experiments has not been undertaken before. The ideal extension of this work would be an application of the employed methods for fractional and stochastic KdV type equations and their variants.

Keywords: linear and non-linear KdV equations; homogeneous; non-homogeneous; variational homotopy perturbation method; classical finite difference method; stability; consistency (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/23/4443/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/23/4443/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:23:p:4443-:d:983450

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().