Biorthogonal Systems Approximating the Solution of the Nonlinear Volterra Integro-Differential Equation
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Springer Open; Hindawi Publishing
Nonlinear Volterra integro-differential equationBiorthogonal systemsBanach spaces
Berenguer, M.I.; Garralda-Guillén, A.I.; Ruiz Galán, M. Biorthogonal Systems Approximating the Solution of the Nonlinear Volterra Integro-Differential Equation. Fixed Point Theory and Applications, 2010: 470149 (2010). [http://hdl.handle.net/10481/33461]
PatrocinadorThis research is partially supported by M.E.C. (Spain) and FEDER, project MTM2006-12533, and by Junta de Andaluca Grant FQM359.
This paper deals with obtaining a numerical method in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach, a sequence of functions which approximate the solution of this type of equation, due to some properties of certain biorthogonal systems for the Banach spaces C[0,1]and C[0,1]2.