Math. J. Interdiscip. Sci.

Mahgoub Deterioration Method and its Application in Solving Duo-combination of Nonlinear PDEs

R Khandelwal, Y Khandelwal and Pawan Chanchal

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  • DOI Number
    https://doi.org/10.15415/mjis.2018.71006
KEYWORDS

Mahgoub deterioration method (MDM), Duocombination of Nonlinear PDE’s

PUBLISHED DATE September, 2018
PUBLISHER The Author(s) 2018. This article is published with open access at www.chitkara.edu.in/publications.
ABSTRACT

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.

INTRODUCTION

Multiple problems in Mathematics are carved by nonlinear partial differential equation. Various researchers are putting efforts to go through these problems finding the correct or almost accurate solutions using diverse procedure. A thousand and one researchers were keen in solving differential equations as well as paid immersion in going through the solution of nonlinear partial differential equations by several approaches. In the past few years, a number of integral transforms have been introduced which help us in solving ODEs and PDEs. We have applied Mahgoub deterioration method to find the exact solution to solve duo-combination of nonlinear partial differential equations (CSNLPDEs). A new Mahgoub Transform are introduced by (Mahgoub, 2016). Dualism between Mahgoub integral transform and some integral transforms have been found (Nidal, 2017). The utility of Mahgoub integral transform method (Fadhil et. al. 2017, Nidal et. al. 2017, Khandelwal et al. 2018) exists in the literature to solve partial differential equations, ordinary differential equations, fractional ordinary differential equation and integral equations. We can see that several problems in the field of Physics and Engineering have been found to show the accuracy of the MDM.

Page(s) 37-44
URL http://dspace.chitkara.edu.in/jspui/bitstream/123456789/759/3/006_MJIS.pdf
ISSN Print: 2278-9561, Online: 2278-957X
DOI https://doi.org/10.15415/mjis.2018.71006
CONCLUSION

The Mahgoub deterioration method (MDM) is used for solving the combination of non linear duo partial differential equation with initial conditions. We found MDM is powerful and easy – to- use analytic tool for PDE’s and thus, the present study highlights the efficiency of the method. Also, we get the exact solution when compared to the result with NDM (Rawashdeh, 2014). This clearly shows that Mahgoub deterioration method can play an important role in future for solving nonlinear PDE’s.

REFERENCES
  • [1] Adomian G. (1991). A review of the decomposition method and some recent results for nonlinear equation, Computers and Mathematics with Applications, 21(5), 101–127.
  • Adomian G. (1984). A new approach to nonlinear partial differential equations, J. Math. Anal. Appl., 102, 420–434.
  • Adomian G. (1994). Solving frontier problems of physic cs: the decomposition method, Kluwer Academic Publishers, Dordrecht.
  • Adomian G. and Rach R. (1983). Nonlinear stochastic differential delay equations. J. Math. Anal. Appl., 91, 94–101.
  • Rawashdeh S. (2014). Mahmoud. Solving Coupled System of Nonlinear PDE’s using the Natural decomposition method, International Journal of Pure and Applied Mathematics, 92(5), 757–776.
  • Mahgoub M. (2016). The New Integral Transform Mahgoub Transform, Advances in Theoretical and Applied Mathematics, 11(4), 391–398.
  • Fadhil R. A. (2017). Convolution for Kamal and Mahgoub transforms, Bulletin of Mathematics and Statistics Research, 5(4), 11–16.
  • Nidal E. and Taha H. (2017). Dualities between Kamal & Mahgoub Integral Transforms and Some Famous Integral Transforms. British Journal of Applied Science & Technology, 20(3), 1–8.
  • Khandelwal Y. (2018). Solution of Fractional Ordinary Differential Equation by Mahgoub Transform, International Journal of Creative Research Thoughts, 6(1), 1494–1499.
  • Khandelwal Y. (2018). Solution of the Blasius Equation by using Adomain Mahgoub Transform, International Journal of Mathematics Trends and Technology, 56(5), 303–306.
  • Hassan Y. Q. and Zhu L. M. (2009). A note on the use of modified Adomian decomposition method for solving singular boundary value problems of higherorder ordinary deferential equations, Communications in Nonlinear Science and Numerical Simulation, 14, 3261–3265.
  • Spiegel M. R. (1965). Theory and Problems of Laplace Transforms, Schaums Outline Series, McGraw–Hill, New York.
  • Wazwaz A. M. (2009). Partial Differential Equations and Solitary Waves Theory, Springer–Verlag, Heidelberg.
  • Elzaki T. M. (2010). 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.
  • Elzaki T. M. (2009). Existence and Uniqueness of Solutions for Composite Type Equation, Journal of Science and Technology, 214–219.
  • Dehghan M. (2007). The solution of coupled Burgers’ equations using Adomian-Pade technique, Applied Mathematics and Computation, 189(2), 1034–1047.
  • Jiao Y. C. (2002). An after treatment technique for improving the accuracy of Adomian’s decomposition method, Computers and Mathematics with Applications, 43(6), 783–798.