Multiderivative Runge-Kutta processes for two-point boundary value problems (Q1060824)

After the preceding paper by the same author [SIAM J. Numer. Anal. 22, 114-126 (1985; reviewed above)], this article discusses 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. For the multiderivative Runge-Kutta processes (really the second derivative processes are given), the order conditions, techniques for reducing these 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. Two numerical examples are shown.