Solving a Nonlinear Volterra Integral Equation in L2 As A Generalized Problem of Moments

Abstract

It will be shown that find an approximate solution y(x) in L2|0,∞) nonlinear Volterra equation integral can be solved applying the techniques of inverse generalized moments problem in two steps writing the Volterra's equation as a Klein-Gordon equation of the form Wxx Wtt-H(x,t), which H(x,t) it is unknown and w(x,t) = y(x)h(t) where h(t)=(t(T-t))2;0≤;t≤T. In a first step, H(x,t) is numerically approximate, and in a second step we numerically approximate the solution y(x) using the H(x,t) previously approximated. The method is illustrated with examples.