Multiderivative Runge-Kutta processes for two-point boundary value problems

Abstract

Abstract.A class of finite difference schemes for the solution of a nonlinear system of first order differential equations with two point boundary conditions which shares properties with Runge-Kutta processes and gap schemes is discussed. The order conditions for the coefficients of these processes, techniques for reducing these order conditions in number and the symmetry conditions are given. A symmetric A-stable eight order process which has second, fourth and sixth order A-stable processes embedded in it is given as an example.