COMPARISON BETWEEN ANALYSIS SOLUTIONS OF VOLTERRA AND FREDHOLM INTEGRAL EQUATIONS OF SECOND KIND
DOI:
https://doi.org/10.53555/eijms.v7i1.53Keywords:
Volterra and Fredholm integral equations, , Adomian decomposition method series solution methodAbstract
Our goal in this paper is to compare and evaluate the accuracy and efficiency between the Volterra and Fredholm integral equations of the second kind with initial condition. We followed the Adomian Decomposition method and series solution method, and we found that the two methods in terms of accuracy in the solution also we found that the Adomian Decomposition method gave us the more accurate solution than the other method, so the Adomian Decomposition method it’s the best one method.
References
. Adomian, G., Solving Frontier Problems of Physics, the Decomposition Method, Kluwer Boston, 1994.
. Adomian, G., Nonlinear Stochastic Operator Equations, Academic Press: San Diego, CA 1986.
. Adomian, G., A Review of the Decomposition Method and Some Recent Results for Nonlinear Equation,Math.
Comput. Modelling, 13(7), pp. 17-43, 1992.
. Adomian, G. & Rach, R., Noise Terms in Decomposition Series Solution, Computers Math. Appl., 24 (1992) 61-64.
. A.M. Wazwaz, A Reliable Treatment for Mixed Volterra-Fredholm Integral Equations, Appl. Math. Comput. 127
(2002) 405-414.
. A.M. Wazwaz, Partial Differential Equations and Solitary Waves Theory, HEP and Springer Beijing and Berlin,
. A.M. Wazwaz, a First Course in Integral Equations, World Scientific Singapore, (1997).
. A.M.Wazwaz, A Reliable Modification of Adomian Decomposition Method,Appl. Math. Comput., 92 (1998) 1-7.
. Cherruault, Y. & Adomian, G., Decomposition methods: A new proof of convergence,Mathl. Comput. Modelling,
(12), pp. 103-106, 1993.
. Cherruault, Y., Saccomandi, G. & Some, B., New Results for Convergence of Adomian’s Method Applied to Integral
Equations,Mathl. Comput. Modelling 16(2), pp. 85-93, 1993.
. H.T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover, New York 1962.
. K. Maleknejad and M. Hadizadeh, a New Computational Method for Volterra-Fredholm Integral Equations, Comput.
Math. Appl., 37 (1999), 1-8.
. Lighthill, M.J., Fourier analysis and Generaralised Functions, Cambridge University Press: Cambridge, 1964.
. R. Kress, Linear Integral Equations, Springer, Berlin, 1999.
. Rahman, M.,Mathematical Methods with Applications, WIT Press: Southampton, UK, 2000
Downloads
Published
Issue
Section
License
Copyright (c) 2021 EPH-International Journal of Mathematics and Statistics
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
