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Approximate Solution of Volterra-Fredholm Integral Equation with Hilbert Kernel

by A. S. Ismail
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 101 - Number 1
Year of Publication: 2014
Authors: A. S. Ismail
10.5120/17648-8434

A. S. Ismail . Approximate Solution of Volterra-Fredholm Integral Equation with Hilbert Kernel. International Journal of Computer Applications. 101, 1 ( September 2014), 1-4. DOI=10.5120/17648-8434

@article{ 10.5120/17648-8434,
author = { A. S. Ismail },
title = { Approximate Solution of Volterra-Fredholm Integral Equation with Hilbert Kernel },
journal = { International Journal of Computer Applications },
issue_date = { September 2014 },
volume = { 101 },
number = { 1 },
month = { September },
year = { 2014 },
issn = { 0975-8887 },
pages = { 1-4 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume101/number1/17648-8434/ },
doi = { 10.5120/17648-8434 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:30:31.661590+05:30
%A A. S. Ismail
%T Approximate Solution of Volterra-Fredholm Integral Equation with Hilbert Kernel
%J International Journal of Computer Applications
%@ 0975-8887
%V 101
%N 1
%P 1-4
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
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
  1. 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).
  2. 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).
  3. H. Brunner, On the numerical solution of nonlinear Volterra- Fredholm integral equations by collocation methods, SIAM j. Numer. Anal. 27 (4), 987-1000, (1990).
  4. L. M. Delves and J. L. Mohamed, Computational Methods for Integral Equations, Cambridge University Press, (1985).
  5. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals & Series and Products, Academic Press, (1980).
  6. H. Guoqiang Asymptotic error expansion for the Nystrom method for a nonlinesr Volterra-Fredholm integral equations, J. Comput. Appl. Math. 59, 49-59, (1995).
  7. 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).
  8. L. Hacia, On approximate solution for integral equations of mixed type, ZAMM. Z. Angew. Math. Mech. 76, 415-416, (1996).
  9. P. J. Kauthen, Continuous time collocation methods for Volterra-Fredholm integral equations, Numer. Math. 56, 409- 424, (1989).
  10. K. Maleknejad and M. Hadizadeh, A new computational method for Volterra-Fredholm integral equations, Comp. and Math. with Appl. 37, 1-8, (1999).
  11. B. G. Pachpatte, On mixed Volterra-Fredholm type integral equations, Indian J. Pure Appl. Math. 17, 488-496, (1986).
Index Terms

Computer Science
Information Sciences

Keywords

Volterra-Fredholm integral equation Hilbert kernel product Nystrom method Numerical treatment.

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