On some numerical iterative methods for Fredholm integral equations with deviating arguments
Keywords:
Fredholm integral equations, deviating arguments, numerical approximations, Altman's algorithm, Mann's iterative algorithm.Abstract
In this paper we develop iterative methods for nonlinear Fredholmintegral equations of the second kind with deviating arguments,
by applying Mann's iterative algorithm. This proves the existence and
the uniqueness of the solution and gives a better error estimate than the
classical Banach Fixed Point Theorem. The iterates are then approximated
using a suitable quadrature formula. The paper concludes with
a numerical example.
References
M. Altman, A Stronger Fixed Point Theorem for Contraction Mappings,
preprint, 1981.
A. Bellen, N. Guglielmi, Solving neutral delay dierential equations with state-dependent delays, J. of Comp. and Appl. Math., 229(2009), 350-362.
V. Berinde, Iterative Approximation of Fixed Points, Lecture Notes in Mathematics, Springer Berlin/Heidelberg/New York, 2007.
S. Micula, An iterative numerical method for Fredholm-Volterra integral
equations of the second kind, Appl. Math. Comput., 270(2015), 935-942,
doi:10.1016/j.amc.2015.08.110.
S. Micula, A fast converging iterative method for Volterra integral equations of the second kind with delayed arguments, Fixed Point Theor. RO, 16(2015), no. 2, 371-380.
A. D. Polyanin, A. V. Manzhirov, Handbook of Integral Equations, CRC Press, Boca Raton/London/New York/Washington D.C., 1998.
S. Prößdorf, B. Silbermann, Numerical Analysis for Integral and Related Operator Equations, Birkhauser Verlag, Basel, 1991.
M. Rahman, Integral Equations and their Applications, WIT Press, Southampton, Boston, 2007.
S. Saha Ray, P. K. Sahu, Numerical methods for solving Fredholm in-
tegral equations of second kind, Abst. Appl. Anal., 2013(2013), 1-17,
http://dx.doi.org/10.1155/2013/426916.
A. M. Wazwaz, Linear and Nonlinear Integral Equations, Methods and Applications, Higher Education Press, Beijing, Springer Verlag, New York, 2011.
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