Kamal decomposition method and its application in solving coupled system of nonlinear PDE’s

Rachana Khandelwal; Padama Kumawat; Yogesh Khandelwal

doi:10.26637/MJM0603/0024

Abstract

In this paper we are solving coupled system of non linear partial differential equations by a new method called Kamal decomposition method (KDM). The new method is coupling of the Kamal transform and the Adomain decomposition method. The generalized solution has been proved. Kamal decomposition method (KDM) is very successful tool for finding the exact solution of linear and non linear partial differential equations. The existence and uniqueness of solution is based on KDM.

Keywords:

Kamal decomposition method (KDM), coupled system of nonlinear PDE’s

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Rachana Khandelwal Department of Mathematics, Maharishi Arvind University, Jaipur, Rajasthan – 609 307, India.
Padama Kumawat Department of Mathematics, Maharishi Arvind University, Jaipur, Rajasthan – 609 307, India.
Yogesh Khandelwal Department of Mathematics, Maharishi Arvind University, Jaipur, Rajasthan – 609 307, India.

Pages: 619-625
Date Published: 01-07-2018
Vol. 6 No. 03 (2018): Malaya Journal of Matematik (MJM)

G. Adomian, A review of the decomposition method and some recent results for nonlinear equation, Computers and Mathematics with Applications, 21(5)(1991), 101127.

G. Adomian, A new approach to nonlinear partial differential equations, J. Math. Anal. Appl., 102(1984), 420434.

G. Adomian, Solving frontier problems of physics: the decomposition method, Kluwer Academic Publishers, Dordrecht, 1994.

G. Adomian, R. Rach, Nonlinear stochastic differential delay equations, J. Math. Anal. Appl., 91(1983), 94-101.

S. M. Rawashdeh, Solving Coupled System of Nonlinear PDE's using the Natural decomposition method, International Journal of Pure and Applied Mathematics, $92(5)(2014), 757-776$.

K. Abdelilah and H. Sedeeg, The New Integral Kamal Transform, Advances in Theoretical and Applied Mathematics, 11(4)(2016), 451-458.

K. Abdelilah, The use of Kamal transform for solving partial differential equations, Advances in Theoretical and Applied Mathematics, 1(2017), 7-13.

${ }^{[8]}$ E. Nidal and H. Taha, Dualities between Kamal & Mahgoub Integral Transforms and Some Famous Integral Transforms, British Journal of Applied Science & Technology, 20(3)(2017), 1-8.

Khandelwal Rachana, Solution of Fractional Ordinary Differential Equation by Kamal Transform, International Journal of Statistics and Applied Mathematics, $3(2)(2018), 279-284$.

Khadelwal Yogesh, Analysis of HIV Model by KTADM, Mathematical Journal of Interdisciplinary Sciences, $6(2)(2018), 181-190$.

Y. Q. Hassan and L. M. Zhu, A note on the use of modified Adomian decomposition method for solving singular boundary value problems of higher-order ordinary deferential equations, Communications in Nonlinear Science and Numerical Simulation, 14(2009), 3261-3265.

M.R. Spiegel, Theory and Problems of Laplace Transforms, Schaums Outline Series, McGraw-Hill, New York, 1965.

A. M. Wazwaz, Partial Differential Equations and Solitary Waves Theory, Springer-Verlag, Heidelberg, 2009.

M. Elzaki Tarig, A. Kilicman and H. Eltayeb, On Existence and Uniqueness of Generalized Solutions for a Mixed-Type Differential Equation, Journal of Mathematics Research, 2(4)(2010), 88-92.

M. Elzaki Tarig, Existence and Uniqueness of Solutions for Composite Type Equation, Journal of Science and Technology, (2009), 214-219.

M. Dehghan, The solution of coupled Burger's equations using Adomian-Pade technique, Applied Mathematics and Computation, 189(2)(2007), 1034-1047.

Y. C. Jiao, An after treatment technique for improving the accuracy of Adomian'ss decomposition method, Computers and Mathematics with Applications, 43(6-7)(2002), $783-798$.