A heuristic to reduce the wrapping effect in the numerical solution ofx′=f(t,x)

The problem of obtaining a realistic guaranteeda posteriori bound on the accumulated error in a computed solution to the initial value problem in ordinary differential equations is difficult, because of the “wrapping” effect. This difficulty can sometimes, but not always, be avoided by making use of coordinate transformations. In this paper we propose that the wrapping effect be reduced by enclosing the accumulated error in a convex polygon of a certain form, and we describe one possible way of choosing the faces of such a polygon. The method is computationally expensive, but provides, in cases where other methods are unable to do so, a bound which does not grow exponentially too fast.