On some numerical iterative methods for Fredholm integral equations with deviating arguments
Dedicated to Professor Gheorghe Coman on the occasion of his 80th anniversary
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 Fredholm integral 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 numerical examples.
Mathematics Subject Classification (2010): 45B05, 47H10, 47N20, 65R20.
References
Altman, M., A Stronger Fixed Point Theorem for Contraction Mappings, preprint, 1981.
Bellen, A., Guglielmi, N., Solving neutral delay differential equations with state-dependent delays, J. of Comp. and Appl. Math., 229(2009), 350-362.
Bellman, R.E., Kalaba, R.E., Quasilinearization and Nonlinear Boundary-Value Problems, Elsevier, New York, 1965.
Berinde, V., Iterative Approximation of Fixed Points, Lecture Notes in Mathematics, Springer Berlin/ Heidelberg/ New York, 2007.
Micula, S., An iterative numerical method for Fredholm-Volterra integral equations of the second kind, Appl. Math. Comput., 270(2015), 935-942.
Micula, S., A fast converging iterative method for Volterra integral equations of the second kind with delayed arguments, Fixed Point Theory, 16(2015), no. 2, 371-380.
Polyanin, A.D., Manzhirov, A.V., Handbook of Integral Equations, CRC Press, Boca Raton/ London/ New York/ Washington D.C., 1998.
Prossdorf, S., Silbermann, B., Numerical Analysis for Integral and Related Operator Equations, Birkhauser Verlag, Basel, 1991.
Rahman, M., Integral Equations and their Applications, WIT Press, Southampton, Boston, 2007.
Saha Ray, S., Sahu, P.K., Numerical methods for solving Fredholm integral equations of second kind, Abst. Appl. Anal., 2013(2013), 1-17.
Wazwaz, A.M., Linear and Nonlinear Integral Equations, Methods and Applications, Higher Education Press, Beijing, Springer Verlag, New York, 2011.
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