Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations

• Autorzy: Appadu Appanah Rao , Kelil Abey Sherif

Identyfikatory

DOI

10.1515/dema-2021-0039

• Języki publikacji: EN

Abstrakty

EN

The KdV equation, which appears as an asymptotic model in physical systems ranging from water waves to plasma physics, has been studied. In this paper, we are concerned with dispersive nonlinear KdV equations by using two reliable methods: Shehu Adomian decomposition method (STADM) and the classical finite difference method for solving three numerical experiments. STADM is constructed by combining Shehu’s transform and Adomian decomposition method, and the nonlinear terms can be easily handled using Adomian’s polynomials. The Shehu transform is used to accelerate the convergence of the solution series in most cases and to overcome the deficiency that is mainly caused by unsatisfied conditions in other analytical techniques. We compare the approximate and numerical results with the exact solution for the two numerical experiments. The third numerical experiment does not have an exact solution and we compare profiles from the two methods vs the space domain at some values of time. This study provides us with information about which of the two methods are effective based on the numerical experiment chosen. Knowledge acquired will enable us to construct methods for other related partial differential equations such as stochastic Korteweg-de Vries (KdV), KdV-Burgers, and fractional KdV equations.

Słowa kluczowe

EN

modified Adomian decomposition method; classical finite difference method; nonlinear KdV equations; blow up

PL

metoda dekompozycji Adomiana; metoda różnic skończonych; nieliniowe równanie różniczkowe; równanie Kortewega-de Vries

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 377--409
• Opis fizyczny: Bibliogr. 44 poz., rys., tab.

Twórcy

autor

Appadu Appanah Rao

• Department of Mathematics and Applied Mathematics, Nelson Mandela University, Gqeberha 6031, South Africa

autor

Kelil Abey Sherif

• Department of Mathematics and Applied Mathematics, Nelson Mandela University, Gqeberha 6031, South Africa

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).