Numerical methods for Volterra equations of the second kind (Q1064042)

The author studies the stability and the order of two numerical methods for the integration of the Volterra equation \(f(x)=g(x)+\int^{x}_{x_ 0}K(x,y,f(y))dy\), \(x\in [x_ 0,X]\). These methods are based on the integration, by using the trapezoidal rule or a backward differentiation type formula, of the differential equations system derived formally by differentiating m-times (m\(\geq 2)\) the given Volterra equation. Numerical examples are given.