A NUMERICAL SOLUTION OF NONLINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS

M. Zarebnia

doi:10.11948/2013008

2013 Volume 3 Issue 1

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M. Zarebnia. A NUMERICAL SOLUTION OF NONLINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2013, 3(1): 95-104. doi: 10.11948/2013008

Citation:

M. Zarebnia. A NUMERICAL SOLUTION OF NONLINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2013, 3(1): 95-104. doi: 10.11948/2013008

A NUMERICAL SOLUTION OF NONLINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS

M. Zarebnia

Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran

Abstract

Abstract

In this paper, a numerical procedure for solving a class of nonlinear VolterraFredholm integral equations is presented. The method is based upon the globally defined sinc basis functions. Properties of the sinc procedure are utilized to reduce the computation of the nonlinear integral equations to some algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the method.
- Nonlinear /
- Volterra-Fredholm /
- integral equations /
- sinc function
MSC: 41A30;45G10

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References

[1]	H.O. Bakodah and M.A. Darwish, On discrete Adomian decomposition method with Chebyshev abscissa for nonlinear integral equations of Hammerstein Type, Advances in Pure Mathematics, 2(2012), 310-313. Google Scholar
[2]	H. Brunner, On the numerical solution of nonlinear Volterra-Fredholm integral equation by collocation methods, SIAM J. Numer. Anal., 27(1990), 987-1000. Google Scholar
[3]	M.A. Darwish, Fredholm-Volterra integral equation with singular kernel, Korean J. Comput. Appl. Math., 6(1999), 163-174. Google Scholar
[4]	M.A. Darwish, Note on stability theorems for nonlinear mixed integral equations, Korean J. Comput. Appl. Math., 6(1999), 633-637. Google Scholar
[5]	M. Ghasemi, M. Tavassoli Kajani and E. Babolian, Numerical solutions of the nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method, Appl. Math. Comput., 188(2007), 446-449. Google Scholar
[6]	J. Lund and K. Bowers, Sinc methods for quadrature and differential equations, SIAM, Philadelphia, PA, 1992. Google Scholar
[7]	C. Minggen and D. Hong, Representation of exact solution for the nonlinear Volterra-Fredholm integral equations, Appl. Math. Comput., 182(2006), 1795-1802. Google Scholar
[8]	Y. Ordokhani, Solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via rationalized Haar functions, Appl. Math. Comput., 180(2006), 436-443. Google Scholar
[9]	B. G. Pachpatte, On a nonlinear Volterra-Fredholm integral equation, Sarajevo J. Math., 16(2008), 61-71. Google Scholar
[10]	F. Stenger, Numerical methods based on Sinc and analytic functions, SpringerVerlag, New York, 1993. Google Scholar
[11]	A. M. Wazwaz, A reliable treatment for mixed Volterra-Fredholm integral equations, Appl. Math. Comput., 127(2002), 405-414. Google Scholar
[12]	S. Yalçinbaş, Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equations, Appl. Math. Comput., 127(2002), 195-206. Google Scholar