Computational Error Estimation

Abstract

The strategy for choosing time steps and mesh sizes is dictated by the a posteriori nature of the global bounds given in Theorem III.1 and Theorem III.2 above. Ideally, an adaptive method should keep the global error below a prescribed tolerance. But global errors are difficult to estimate. Thus, a standard approach is to adjust the discretization parameters during the integration in order to restrict the local truncation error. One would hope that smaller local errors lead also to a decrease of the global error — a property which is known as tolerance proportionality in the pure ODE case [155].