Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31742
Numerical Solution of Hammerstein Integral Equations by Using Quasi-Interpolation

Authors: M. Zarebnia, S. Khani


In this paper first, a numerical method based on quasiinterpolation for solving nonlinear Fredholm integral equations of the Hammerstein-type is presented. Then, we approximate the solution of Hammerstein integral equations by Nystrom’s method. Also, we compare the methods with some numerical examples.

Keywords: Hammerstein integral equations, quasi-interpolation, Nystrom’s method.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4284


[1] Akbar H.Borzabadi and Omid S. Fard,A Numerical scheme for a class of nonlinear Fredholm integral equation of the second kind, Journal of Computational and Applied Mathematics 232(2009)449 − 454.
[2] K.E. Atkinson, The numerical solution of integral equation of the second kind, Cambridge University press, 1997.
[3] L.M. Delves and J.L. Mohamed, Computational methods for integral equation, Cambridge University press, 1985.
[4] L.M. Delves and J. Wash, Numerical solution of integral equation, Oxford University press, 1974.
[5] M. Javidi and A. Galbabai, Modified homotopy perturbation method for solving non-linear Fredholm integral equations, Chaos, Solitons and Fractals. 40(2009)1408 − 1412.
[6] R. Kress, Linear Integral Equations, 2nd ed., Springer, Berlin, 1999.
[7] V. Maz’ya, A new approximation method and its applications to the calculation of volume potentials, boundary point method. in: 3. DFGKolloquium des DFG-Forschungsschwerpunktes Randelementmethoden, 1991.
[8] V. Maz’ya, G. Schmidt, On approximate approximations using Gaussian Kernels, IMA J. Num. Anal. 16(1996)13 − 29.
[9] V. Maz’ya, G. Schmidt, Approximate Approximations, Mathematical Surveys and Monographs, vol. 141, AMS, 2007.
[10] F. Muller and W. Varhorn, On approximation and numerical solution of Fredholm interal equation of second kind using quasi-interpolation, Applied Mathematics and Computation 217(2011)6409 − 6416.