International Journal of Partial Differential Equations and Applications
ISSN (Print): 2376-9548 ISSN (Online): 2376-9556 Website: http://www.sciepub.com/journal/ijpdea Editor-in-chief: Mahammad Nurmammadov
Open Access
Journal Browser
Go
International Journal of Partial Differential Equations and Applications. 2020, 8(1), 6-12
DOI: 10.12691/ijpdea-8-1-2
Open AccessArticle

Elzaki Substitution Method for Solving Nonlinear Partial Differential Equations with Mixed Partial Derivatives Using Adomian Polynomial

Mousumi Datta1, , Umme Habiba1 and Md. Babul Hossain1

1Department of Mathematics, Mawlana Bhashani Science and Technology University, Santosh, Tangail, Bangladesh

Pub. Date: September 27, 2020

Cite this paper:
Mousumi Datta, Umme Habiba and Md. Babul Hossain. Elzaki Substitution Method for Solving Nonlinear Partial Differential Equations with Mixed Partial Derivatives Using Adomian Polynomial. International Journal of Partial Differential Equations and Applications. 2020; 8(1):6-12. doi: 10.12691/ijpdea-8-1-2

Abstract

In this paper we apply a new method, named Elzaki Substitution Method to solve nonlinear homogeneous and nonhomogeneous partial differential equations with mixed partial derivatives, which is based on Elzaki Transform. The proposed method introduces also Adomian polynomials and the nonlinear terms can be handled by the use of this polynomials. The proposed method worked perfectly to find the exact solutions of partial equations with mixed partial derivatives without any need of linearization or discretization in comparison with other methods such as Method of Separation of Variables (MSV) and Variation Iteration Method (VIM). Some illustrative examples are given to demonstrate the applicability and efficiency of proposed method.

Keywords:
Partial Differential Equations Exact Solution Mixed Partial Derivatives Elzaki Transform Elzaki Substitution Method Adomian polynomial

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Elzaki, T.M., The new integral transform “Elzaki Transform”. Global Journal of Pure and Applied Mathematics, 7(1), pp.57-64. 2011.
 
[2]  Elzaki, T.M., Application of new transform “Elzaki transform” to partial differential equations. Global Journal of Pure and Applied Mathematics, 7(1), pp.65-70. 2011.
 
[3]  Elzaki, T.M., On the New Integral Transform “ELzaki Transform” Fundamental Properties Investigations and Applications. Global Journal of Mathematical Sciences: Theory and Practical, 4(1), pp.1-13. 2012.
 
[4]  Elzaki, T.M., On Some Applications of New Integral Transform ''Elzaki Transform''. The Global Journal of Mathematical Sciences: Theory and Practical, 4(1), pp.15-23. 2012.
 
[5]  Elzaki, T.M. and Ezaki, S.M., On the Elzaki transform and ordinary differential equation with variable coefficients. Advances in Theoretical and Applied Mathematics, 6(1), pp.13-18. 2011.
 
[6]  Elzaki, T.M. and Elzaki, S.M., On the Tarig transform and system of partial differential equations. Applied Mathematics, Elixir Appl. Math, 42, pp.6373-6376. 2012.
 
[7]  Hussain, F., Solution of 1-dimensional Wave equation by Elzaki Transform. Internation Journal of Multidisciplinary Researcs and Development, 4(10), pp.64-67. 2017.
 
[8]  Elzaki, T.M., On the Elzaki transform and higher order ordinary differential equations. Advances in Theoretical and Applied mathematics, 6(1), pp.107-113. 2011.
 
[9]  Kim, H., A note on the shifting theorems for the Elzaki transform. Int. J. of Math. Anal, 8, pp.481-488. 2014.
 
[10]  Kilicman A and Eltayeb H., A Note of Integral Transform and Partial Differential Equations, Applied Mathematical Sciences, 4(3), pp109-118. 2010.
 
[11]  Arabia, J.S., Solution of partial integro-differential equations by Elzaki transform method. Applied Mathematical Sciences, 9(6), pp.295-303. 2015.
 
[12]  Elzaki, T.M. and Ezaki, S.M., On the solution of integro-differential equation systems by using Elzaki transform. Global Journal of Mathematical Sciences: Theory and Practical, 3(1), pp.13-23. 2011.
 
[13]  Nuruddeen, R.I., Elzaki decomposition method and its applications in solving linear and nonlinear Schrodinger equations. Sohag Journal of Mathematics, 4(2), pp.1-5. 2017.
 
[14]  Adam, B.A., A comparative study of Adomain decomposition method and the new integral transform" Elzaki transform". International Journal of Applied Mathematics Research, 4(1), p.8. 2015.
 
[15]  Handibag, S.S. and Karande, B.D., An application for nonlinear partial differential equations involving mixed partial derivatives by Laplace substitution method. In AIP Conference Proceedings. American Institute of Physics (Vol. 1637, No. 1, pp. 384-394).
 
[16]  Hossain, M. B and Mousumi Datta. Solutions of Linear Partial Differential Equations with Mixed Partial Derivatives by Elzaki Substitution Method, American Journal of Computational and Applied Mathematics, 8(3),pp.59-64. 2018.