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A sequential approach for solving the Fredholm integro-differential equation. (English) Zbl 1241.65118
Summary: A numerical approximation method for the solution of Fredholm integro-differential equations is presented. The method provides a sequential solution and makes use of appropriate Schauder bases in adequate Banach spaces of continuous functions as well as of classical fixed-point results. The method is computationally attractive and some numerical examples are provided to illustrate its high accuracy.

65R20Integral equations (numerical methods)
45B05Fredholm integral equations
45G10Nonsingular nonlinear integral equations
45J05Integro-ordinary differential equations
Full Text: DOI
[1] Berenguer, M. I.; Fortes, M. A.; Garralda-Guillem, A. I.; Galán, M. Ruiz: Linear Volterra integro-differential equation and Schauder bases, Appl. math. Comput. 159, No. 2, 495-507 (2004) · Zbl 1068.65143 · doi:10.1016/j.amc.2003.08.132
[2] M.I. Berenguer, M.V. Fernández Muñoz, A.I. Garralda-Guillem, M. Ruiz Galán, Numerical treatment of fixed point applied to the nonlinear Fredholm integral equation, Fixed Point Theory Appl., Article ID 735638, 8 p., doi:10.1155/2009/735638, 2009. · Zbl 1177.65082 · doi:10.1155/2009/735638
[3] M.I. Berenguer, A.I. Garralda-Guillem, M. Ruiz Galán, Biorthogonal systems approximating the solution of the nonlinear Volterra integro-differential equation, Fixed Point Theory Appl., Article ID 470149, 9 p., doi:10.1155/2010/470149, 2010. · Zbl 1198.65079 · doi:10.1155/2010/470149
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