Chitkara University Publications

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

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.

Author(s):

  • R Khandelwal, Department of Mathematics, Maharishi Arvind University, Jaipur, 302 041, Rajasthan, India
  • Y Khandelwal, Department of Mathematics, Maharishi Arvind University, Jaipur, 302 041, Rajasthan, India
  • Pawan Chanchal, Department of mathematics, Government college, kekri, Ajmer, 305 406, Rajasthan, India

DOI: 

Keywords: 

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

References:

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 higher-order ordinary differential equations, Communications in Nonlinear Science and Numerical Simulation, 14, 3261–3265.

Spiegel M. R. (1965). Theory and Problems of Laplace Transforms, Schaum’s 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.

 

 

0 0 votes
Article Rating
Subscribe
Notify of
0 Comments
Inline Feedbacks
View all comments
CHITKARA UNIVERSITY ADMINISTRATIVE OFFICE SARASWATI KENDRA, PO Box No. 70 SCO – 160-161,Sector – 9C, Chandigarh – 160009, India. +91-172-2741000, +91-172-4691800 chitkarauniversitypublications@chitkara.edu.in

    0
    Would love your thoughts, please comment.x
    ()
    x