Minimising Truncation Error in Finite Difference Approximations to Ordinary Differential Equations

Abstract

It is shown that the error in setting up a class of finite difference approximations is of two kinds: a quadrature error and an interpolation error. In many applications the quadrature error is dominant, and it is possible to take steps to reduce it. In the concluding section an attempt is made to answer the question of how to find a finite difference formula which is best in the sense of minimising the work which has to be done to obtain an answer to within a specified tolerance.