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Approximate Solution of Volterra-Fredholm Integral Equation with Hilbert Kernel
International Journal of Computer Applications
© 2014 by IJCA Journal
Volume 101 - Number 1
Year of Publication: 2014
|
10.5120/17648-8434 |
A S Ismail. Article: Approximate Solution of Volterra-Fredholm Integral Equation with Hilbert Kernel. International Journal of Computer Applications 101(1):1-4, September 2014. Full text available. BibTeX
@article{key:article,
author = {A. S. Ismail},
title = {Article: Approximate Solution of Volterra-Fredholm Integral Equation with Hilbert Kernel},
journal = {International Journal of Computer Applications},
year = {2014},
volume = {101},
number = {1},
pages = {1-4},
month = {September},
note = {Full text available}
}
Abstract
In this work, We use numerical technique to reduce the Volterra- Fredholm integral equation to a linear system of Fredholm integral equations of the second kind and we apply the product Nystrom method to solve this system of integral equations to get the approximate solution of Volterra-Fredholm integral equation. The results are compared with the exact solution of the integral equation.
References
- M. A. Abdou, Khamis I. Mohamed and A. S. Ismail, On the numerical solutions of Fredholm-Volterra integral equation, Appl. Math. Comp. 146, 713-728, (2003).
- M. A. Abdou, Khamis I. Mohamed and A. S. Ismail, Toeplitz Matrix and product Nystrom methods for solving the singular integral equation, Le Matematiche LVII-Fasc. I, 21-37, (2002).
- H. Brunner, On the numerical solution of nonlinear Volterra- Fredholm integral equations by collocation methods, SIAM j. Numer. Anal. 27 (4), 987-1000, (1990).
- L. M. Delves and J. L. Mohamed, Computational Methods for Integral Equations, Cambridge University Press, (1985).
- I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals & Series and Products, Academic Press, (1980).
- H. Guoqiang Asymptotic error expansion for the Nystrom method for a nonlinesr Volterra-Fredholm integral equations, J. Comput. Appl. Math. 59, 49-59, (1995).
- H. Guoqiang and Z. Liqing, Asymptotic expansion for the trapezoidal Nystrom method of linesr Volterra-Fredholm integral equations, J. Comput. Appl. Math. 51 (3), 339-348, (1994).
- L. Hacia, On approximate solution for integral equations of mixed type, ZAMM. Z. Angew. Math. Mech. 76, 415-416, (1996).
- P. J. Kauthen, Continuous time collocation methods for Volterra-Fredholm integral equations, Numer. Math. 56, 409- 424, (1989).
- K. Maleknejad and M. Hadizadeh, A new computational method for Volterra-Fredholm integral equations, Comp. and Math. with Appl. 37, 1-8, (1999).
- B. G. Pachpatte, On mixed Volterra-Fredholm type integral equations, Indian J. Pure Appl. Math. 17, 488-496, (1986).