Abstract
In this paper, a numerical method for solving the linear and nonlinear Fredholm integral equations is proposed. In this method the solution of these equations are approximated by Romberg quadrature rule. Also, the convergence of the method is proved and some numerical examples are solved to investigate the applicability and simplicity of the method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brunner, H., van der Houwen, P.J.: The Numerical Solution of Volterra Equations, CWI Monographs 3. North-Holland, Amsterdam (1986)
Jerri, A.J.: Introduction to Integral Equation with Applications. Wiley, Oxford (1932)
Kaltenbacher, B., Neubauer, A., Scherezer, O.: Iterative Regularization Method for Nonlinear Ill-Posed Problems. Water de Gruyter, Berlin (2008)
Katani, R., Shahmorad, S.: The block by block method with Romberg quadrature for the solution of nonlinear Volterra integral equations on large intervals. Ukrain. Math. J. 64(7), 1050–1063 (2012)
Lepik, U., Tamme, E.: Solution of nonlinear Fredholm integral equations via the Haar wavelet method. Proc. Estonian Acad. Sci. Phys. Math. 56, 17–27 (2007)
Martin, P.A., Farina, L.: Radiation of water waves by a heaving submerged horizontal disc. J. Fluid. Mech. 337, 365–379 (1997)
Shirin, A., Islam, M.S.: Numerical solution of Fredholm integral equations using Bernstein polynomials. Progress Inform. Comput. 2010, 423–431 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Katani, R. Numerical solution of the Fredholm integral equations with a quadrature method. SeMA 76, 271–276 (2019). https://doi.org/10.1007/s40324-018-0175-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40324-018-0175-z