Abstract :
The numerical solution of Initial value problems (IVPs) for ODEs is one of the fundamental problems in scientific comp-utation. Today, there are many well-estab-lished algorithms for approximate solution of IVPs. However, traditional integration methods usually provide only approximate values for the solution. Precise error bounds are rarely available. The error estimates, which are sometimes delivered, are not guaranteed to be accurate and are sometimes unreliable. In contrast, reliablep; integration computes guaranteed bounds for the flow of an ODE, including all discretization and roundoff errors in the computation. Originated by Moore in the 1960s [33], interval computations are a particularly useful tool for this purpose. There is a vast literature on interval methods for verified integration [2, 5, 25, 27, 28, 33, 42]. But there are still many open questions. The results of interval arithmetic computations are often impaired by overestimation caused by the dependency problem and by the wrapping effect. ln verified integration, overestimation may degrade the computed enclosure of the flow, enforce miniscule step sizes, or even bring about premature abortion of an integration.
