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Numerical Solution of the Fredholme-Volterra Integral Equation by the Sinc Function

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DOI: 10.4236/ajcm.2012.22019    4,028 Downloads   8,428 Views   Citations

ABSTRACT

In this paper, we use the Sinc Function to solve the Fredholme-Volterra Integral Equations. By using collocation method we estimate a solution for Fredholme-Volterra Integral Equations. Finally convergence of this method will be discussed and efficiency of this method is shown by some examples. Numerical examples show that the approximate solutions have a good degree of accuracy.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

A. Shamloo, S. Shahkar and A. Madadi, "Numerical Solution of the Fredholme-Volterra Integral Equation by the Sinc Function," American Journal of Computational Mathematics, Vol. 2 No. 2, 2012, pp. 136-142. doi: 10.4236/ajcm.2012.22019.

References

[1] S. Fayazzadeh and M. Lotfi, “Collocation Method for Fredholm-Volterra Integtral Equations with Weakly Kernels,” International Journal of Mathematical Modelling & Computations, Vol. 1, 2011, pp. 59-58
[2] A. Shahsavaran, “Numerical Solution of Nonlinear Fredholm-Volterra Integtral Equations via Piecewise Constant Function by Collocation Method,” American Journal of Computational Mathematics, Vol. 1, No. 2, 2011, pp. 134- 138.
[3] F. Stenger, “Numerical Methods Based on the Whittaker Cardinal or Sinc Functions,” SIAM Review, Vol. 23, No. 2, 1981, pp. 165-224.
[4] J. Lund, “Symmetrization of the Sinc-Galerkin Method for Boundary Value Problems,” Mathematics of Computation, Vol. 47, No. 176, 1986, pp. 571-588.
[5] B. Bialecki, “Sinc-Collocation Methods for Two-Point Boundary Value Problems,” IMA Journal of Numerical Analysis, Vol. 11, No. 3, 1991, pp. 357-375. doi:10.1093/imanum/11.3.357
[6] N. Eggert, M. Jarrat and J. Lund, “Sinc Function Computation of the Eigenvalues of Sturm—Liouville Problems,” Journal of Computational Physics, Vol. 69, No. 1, 1987, pp. 209-229. doi:10.1016/0021-9991(87)90163-X
[7] M. A. Abdou and O. L. Mustafa, “Fredholm-Volterra Integral Equation in the Contact Problem,” Applied Mathematics and Computation, Vol. 138, No. 2-3, 2002, pp. 1- 17.
[8] J. Land and K. Bowers, “Sinc Methods for Quadrature and Differential Equations,” Society for Industrial and Applied Mathematics, Philadelphia, 1992.
[9] F. Stenger, “Numerical Methods Based on Sinc and Analytic Function,” Springer-Verlag, New York, 1993.
[10] J. Rashidinia and M. Zarebnia, “Solution of a Volterra Integral Equation by the Sinc-Collocation Method,” Journal of Computational and Applied Mathematics, Vol. 206, No. 2, 2007, pp. 801-813. doi:10.1016/j.cam.2006.08.036

  
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