Mathematics and Statistics Vol. 8(2A), pp. 9 - 16
DOI: 10.13189/ms.2020.081302
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Approximate Analytical Solutions of Nonlinear Korteweg-de Vries Equations Using Multistep Modified Reduced Differential Transform Method

Che Haziqah Che Hussin ^1,2,*, Ahmad Izani Md Ismail ¹, Adem Kilicman ³, Amirah Azmi ^1
1 School of Mathematical Sciences, University of Science, Malaysia
² Preparatory Centre of Science and Technology, Universiti Malaysia Sabah, Malaysia
³ Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Malaysia

ABSTRACT

This paper aims to propose and investigate the application of Multistep Modified Reduced Differential Transform Method (MMRDTM) for solving the nonlinear Korteweg-de Vries (KdV) equation. The proposed technique has the advantage of producing an analytical approximation in a fast converging sequence with a reduced number of calculated terms. MMRDTM is presented with some modification of the reduced differential transformation method (RDTM) which is the nonlinear term is replaced by related Adomian polynomials and then adopting a multistep approach. Consequently, the obtained approximation results do not only involve smaller number of calculated terms for the nonlinear KdV equation, but also converge rapidly in a broad time frame. We provided three examples to illustrates the advantages of the proposed method in obtaining the approximation solutions of the KdV equation. To depict the solution and show the validity and precision of the MMRDTM, graphical inputs are included.

KEYWORDS
Adomian Polynomials, Multistep Approach, Nonlinear Korteweg-de Vries Equation, Reduced Differential Transform Method

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Che Haziqah Che Hussin , Ahmad Izani Md Ismail , Adem Kilicman , Amirah Azmi , "Approximate Analytical Solutions of Nonlinear Korteweg-de Vries Equations Using Multistep Modified Reduced Differential Transform Method," Mathematics and Statistics, Vol. 8, No. 2A, pp. 9 - 16, 2020. DOI: 10.13189/ms.2020.081302.

(b). APA Format:
Che Haziqah Che Hussin , Ahmad Izani Md Ismail , Adem Kilicman , Amirah Azmi (2020). Approximate Analytical Solutions of Nonlinear Korteweg-de Vries Equations Using Multistep Modified Reduced Differential Transform Method. Mathematics and Statistics, 8(2A), 9 - 16. DOI: 10.13189/ms.2020.081302.