Logarithmic Reduction of the Wrapping Effect with Application to Ordinary Differential Equations

Abstract

For moderate-sized problems one can obtain numerical solutions with rigorous error bounds using interval techniques. However, for systems of ODEs these error bounds often exhibit spurious exponential growth due to the inadequacy of boxes for representing sets of solution values in more than one dimension, a phenomenon known as wrapping. In this paper we consider the use of odd/even reduction to reduce the exponential growth to polynomial growth. Numerical results confirm the success of this technique for initial value problems.