Numerical solution of linear differential equations and Volterra's integral equation using Lobatto quadrature formula

Abstract

This paper describes a one-step method based on the Lobatto four-point quadrature formula for the numerical solution of the differential equation [equation: see PDF] . The method has been extended to the linear differential equation [equation: see PDF] and to Volterra's linear integral equation of the second kind. In the case of ordinary linear second-order differential equation, a computational and theoretical comparison of the new method with other methods is also discussed.