Solution of non-linear integro-differential equations by using modified Laplace transform Adomian decomposition method
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Abstract
In last few decades, integro-differential equations are used in various fields of sciences and engineering. Recently most of researchers have taken considerable effort to the study of exact and numerical solutions of the linear, nonlinear ordinary, or partial differential equations. In this paper, we have discussed the Modified Laplace Transform Adomian Decomposition Method (MLTADM) which is the combination of Laplace transform and Adomian decomposition method to solve the second and third-order nonlinear integro-differential equations. The main advantage of this method is that it gives an analytical solution. The method overcomes the difficulties arising in calculating the Adomian polynomials. The efficiency of the method was tested on some numerical examples, and the results show that the method is easier than many other numerical techniques. It is also observed that (MLTADM) is a reliable tool for the solution of linear and nonlinear integro-differential equations.
Keywords:
Laplace Transform, Adomian decomposition method, Volterra-Fredholm integro-differential equation, Non-Linear Volterra integral equationMathematics Subject Classification:
Mathematics- Pages: 1199-1203
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
M. Dehghan, J. Manafian, and A. Saadatmandi, The solution of the linear fractional partial differential equations using the homotopy analysis method, Z. Naturforsch, $65(2010), 935-949$.
M. Hussain and M. Khan, Modified Laplace decomposition method, Appl.Math. Sci., 4(2010), 1769-1783.
S. Shahmorad, Numerical solution of the general form linear Fredholm-Volterra integro-differential equations by the Tau method with an error estimation, Appl. Math. Comput., 167(2005), 1418-1429.
N. Bildik, A comparison between Adomian decomposition and Tau methods, Abstract and Applied Analysis, $2(2013), 124-135$.
S. Alkan and V. F. Hatipoglu, Approximate solutions of Volterra-Fredholm integro-differential equations of fractional order, Tbilisi Math. J., 10(2017), 1-13.
M. Al-Mazmumy and H. Al-Malki, Some modifications of adomian decomposition methods for nonlinear partial differential equations, Int. J. Res. Agricul. Sci., 23(2015), $164-173$.
S. Agarwal, N. Sharma, and R. Chauhan, Application of Mahgoub transform for solving linear Volterra integral equations of first kind, Global Journal of Engineering Science and Researches, 5(9)(2018), 154-161.
R.B. Thete, Temperature distribution of an inverse steady state thermo elastic problem of thin rectangular plate by numerical method, IOSR Journal of Mathematics, $11(1)(2015), 36-39$.
Tarik M. Elzaki Adil Mousa, Solution of volterra integro differential equation by triple Laplace Transform, Irish International Journal of Science & Research, 3(4)(2019), $1-10$.
R.B. Thete, Estimation of temperature distribution and thermal stress analysis of composite circular rod by finite element method, Elixir Appl. Math., 95(2016), 1-10.
R.B. Thete and Arihant Jain, Analytical solution of linear Volterr Integro- differential equation of first and second kind by Laplace transform, Journal of Emerging Technologies and Innovative Research, 6(1)(2019), $152-155$.
P. K. Kythe and P. Puri, Computational Methods for Linear Integral Equations, Birkhauser, Boston, 2002.
C. T. H. Baker, The Numerical Treatment of Integral Equations, Oxford University Press, 1977.
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