Math. J. Interdiscip. Sci.

Mahgoub Deterioration Method and its Application in Solving Duo-combination of Nonlinear PDE's

Rachana Khandelwal and Yogesh Khandelwal, Pawan Chanchal

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Mahgoub deterioration method (MDM), Duo-combination of Nonlinear PDE’s

PUBLISHED DATE September 6, 2018
PUBLISHER The Author(s) 2018. This article is published with open access at

This paper aims to solve Duo-combination of non linear partial differential equations by a latest approach called Mahgoub deterioration method (MDM). The latest technique is mix of the Mahgoub transform furthermore the, Adomian deterioration method. The generalized solution has been proved. Mahgoub deterioration method (MDM) is a very successful tool for finding the correct solution of linear and non linear partial differential equations. The continuance and uniqueness of solution is based on MDM.

Page(s) 37-44
ISSN Print: 2278-9561, Online: 2278-957X
  • G. Adomian, A review of the decomposition method and some recent results for nonlinear equation, Computers and Mathematics with Applications, 21(5), 101–127, (1991).
  • G. Adomian, A new approach to nonlinear partial differential equations, J. Math. Anal. Appl., 102(1984), 420–434.
  • G. Adomian, Solving frontier problems of physic cs: the decomposition method, Kluwer Academic Publishers, Dordrecht, (1994).
  • G. Adomian and R. Rach, Nonlinear stochastic differential delay equations. J. Math. Anal. Appl., 91, 94–101, (1983).
  • Mahmoud S. Rawashdeh and Shehu Maitama, Solving Coupled System of Nonlinear PDE’s using the Natural decomposition method, International Journal of Pure and Applied Mathematics, 92(5), 757–776, (2014).
  • Mohand M. Abdelrahim Mahgoub, The New Integral Transform Mahgoub Transform, Advances in Theoretical and Applied Mathematics, 11(4), 391–398, (2016).
  • Roaa Aziz Fadhil, Convolution for Kamal and Mahgoub transforms, Bulletin of Mathematics and Statistics Research, 5(4), 11–16, (2017).
  • Nidal E. Hassan Taha, R. I. Nuruddeen and Abdelilah Kamal H. Sedeeg, Dualities between Kamal & Mahgoub Integral Transforms and Some Famous Integral Transforms. British Journal of Applied Science & Technology, 20(3), 1–8, (2017).
  • Yogesh Khandelwal, Shailender Singh and Rachana khandelwal, Solution of Fractional Ordinary Differential Equation by Mahgoub Transform, International Journal of Creative Research Thoughts, 6(1), 1494–1499, (2018).
  • Yogesh Khandelwal, Baba Alhaji Umar and Padama Kumawat, Solution of the Blasius Equation by using Adomain Mahgoub Transform, International Journal of Mathematics Trends and Technology, 56(5), 303–306 (2018).
  • Yahya Qaid Hassan and Liu Ming 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, 3261–3265, (2009).
  • Murray R. Spiegel, Theory and Problems of Laplace Transforms, Schaums Outline Series, McGraw–Hill, New York (1965).
  • Abdul-Majid Wazwaz, Partial Differential Equations and Solitary Waves Theory, Springer–Verlag, Heidelberg, (2009).
  • Tarig Elzaki, Adem Kilicman and Hassan Eltayeb, On Existence and Uniqueness of Generalized Solutions for a Mixed-Type Differential Equation, Journal of Mathematics Research, 2(4), 88–92, (2010).
  • T. M. Elzaki, Existence and Uniqueness of Solutions for Composite Type Equation, Journal of Science and Technology, 214–219 (2009).
  • Mehdi Dehghan, Asgar Hamidi and Mohammad Shakourifar, The solution of coupled Burgers’ equations using Adomian-Pade technique, Applied Mathematics and Computation, 189(2), 1034–1047, (2007).
  • Y. C. Jiao, Y. Yamamoto, C. Dang and Y. Hao, An after treatment technique for improving the accuracy of Adomian’s decomposition method, Computers and Mathematics with applications 43(6-7), 783-798, (2002)