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Linear Volterra integro-differential equation and Schauder bases. (English) Zbl 1068.65143
Upon rewriting the initial-value problem for the linear Volterra integro-differential equation $y'(t)= q(t)+ p(t) y(t)+ q(t)+ \int^t_0 K(t, s)y(s)\,ds,\quad t\in [0,1],$ as a second-kind Volterra integral equation, the authors show that instead of resorting to the Banach fixed-point theorem for generating its solution $$y$$, the use of Schauder bases for the spaces $$C([0, 1])$$ and $$C([0, 1]^2)$$ yields computable approximations for $$y$$. A simple example illustrates the convergence analysis. No comparison with other global numerical methods (e.g. collocation) is given.

##### MSC:
 65R20 Numerical methods for integral equations 45J05 Integro-ordinary differential equations
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##### References:
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