A fourth order multiderivative method for linear second order boundary value problems

Fourth order methods are developed and analysed for the numerical solution of linear second order boundary value problems.

The methods are developed by replacing the exponential terms in a three-point recurrence relation by Padé approximants.

The derivations of second order and sixth order methods from the recurrence relation are outlined briefly.

One method is tested on two problems from the literature, one of which is mildly nonlinear.