Linear Volterra integro-differential equation and Schauder bases

摘要

In this paper we present a numerical method to approximate the solution of the linear Volterra integro-differential equation. By making use of the expression of a function of the Banach space C([0,1]) in terms of a basis Schauder, we are able to define a sequence of functions which approximate (in the uniform sense) the solution of such equation. Likewise, we study the error committed in each approximation. Some advantages that this method possess are that it is not necessary to solve linear equation systems and moreover, the involved integrals are immediate.