Laplace Substitution – Variational Iteration Method for Solving Goursat Problems Involving Mixed Partial Derivatives
American Journal of Mathematical and Computer Modelling
Volume 4, Issue 1, March 2019, Pages: 16-20
Received: Feb. 26, 2019;
Accepted: Apr. 4, 2019;
Published: May 10, 2019
Views 55 Downloads 15
Ali Al-Fayadh, Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Baghdad, Iraq
Dina Saad Faraj, Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Baghdad, Iraq
Follow on us
This paper will investigate a method to achieve the exact solution of special type of nonlinear partial differential equations (NLPDEs) involving mixed partial derivatives. This proposed method named as Laplace substitution - Variation iteration method (LS-VIM). The method exploits the properties of Laplace substitution method and the Variational iteration method to find the exact solution for Goursat problem involving mixed partial derivatives. In addition, this paper emphasizes the effectiveness of the LS-VIM by solving two examples. The results show that the exact solution can be achieved from a single iteration of the propose method.
Laplace Transforms, Laplace Substitution Method, Variation Iteration Method, Mixed Partial Derivatives, Goursat Problems
To cite this article
Dina Saad Faraj,
Laplace Substitution – Variational Iteration Method for Solving Goursat Problems Involving Mixed Partial Derivatives, American Journal of Mathematical and Computer Modelling.
Vol. 4, No. 1,
2019, pp. 16-20.
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Ahmad J, Mushtaq M. Exact Solution of Linear and Non-linear Goursat Problems. Univers J Comput Math. 2015; 3 (1): 14-17..
A. AL-Fayadh and H. Khawwan, “Variation Iteration Transform Method For Solving Burger and Coupled Burgers eqution, ” ARPN J. Eng. Appl. Sci., vol. 12, no. 23, pp. 6926–6932, 2017.
Evans D., Sanusi B. Numerical Solution of the Goursat Problem By A Nonlinear Trapezoidal Forula. Appl Math Lett. 1988; I (3): 221-223.
Handibag S., Karande BD. An Application for Nonlinear Partial Differential Equations Involving Mixed Partial Derivatives by Laplace Substitution Method. In: 10th International Conference on Mathematical Problems in Engineering, Aerospace and Science. AIP Conf. Proc. Vol 1637; 384-394, (2014).
J.T. Day, A Runge–Kutta method for the numerical solution of the Goursat problem in hyperbolic partial differential equations.
Muhammad Aslam Noor ,Syed Tauseef Mohyud-Din.Modified Variational Iteration Method for Goursat and Laplace Problems.Appl Sciences Journal 4 (4): 487-498, 2008.
SharafMohmoud, Mohamed Gubara. Reduced Differential Transform Method.Appl Math, 2016, 7, 1049-1056
Taghvafard H, Erjaee GH. Two-dimensional Differential Transform Method for Solving Linear and Non-linear Goursat Problem. Int J Math Comput Phys Electr Comput Eng. 2010; 4 (3):432-435.
Usman M, Zubair T, Ali U, Mohyud-din ST. On Goursat Problems. Int J Mod Math Sci. 2012; 3 (3): 63-76.
Wazwaz A. The variational iteration method for a reliable treatment of the linear and the nonlinear Goursat problem. Appl Math Comput. 2007; 193: 455-462
Handibag S, Karande BD. Laplace Substitution Method for Solving Partial Differential Equations Involving Mixed Partial Derivatives. Int J Comput Eng Res. 2012; 2 (4): 1049-1052.
Handibag S, Karande B. LAPLACE SUBSTITUTION METHOD FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS INVOLVING MIXED PARTIAL DERIVATIVES. Int J Pure Appl Math. 2012; 78 (7): 973-979.
Handibag S., Karande B. Laplace Substitution Method for n th Order Linear and Non-Linear PDE ’ s Involving Mixed Partial Derivatives. Int Res J Eng Technol. 2015; 2 (9): 378-388.
Pandey PK. A Finite Difference Method for Numerical Solution of Goursat Problem of Partial Differential Equation. Open Access Libr J. 2014; 1: 1-6.
Ramadan MA, Raslan KR, Hadhoud AR, Mesrega AK. A Substitution Method for Partial Differential Equations Using Ramadan Group Integral Transform. Asian Res J Math. 2017; 7 (4): 1-10.