Abstract
The general n-th order integro-differential equation (1)[equation] where the vector y(x) represents the vector of y(x) and its n-1 derivatives (2)[equation] has a unique family of solutionsy (x ), with one solution for each initial condition y(xo) = Yo One-step methods for numerically approximating these solutions are defined as satisfying (3)[equation] These methods are shown to converge to y(x) iff φand ψ are consistent with the integro-differential equation (1), and several numerical examples are developed as demonstrations. The rate of convergence for y(x) is O[h2n-min(p, q-1, r-1)]; where p, q, r are the orders of the highest derivatives actually used in f, K(x), and K(s) respectively.
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