A New Test Frame for Ordinary Differential Equation

Benchmarking of ODE methods has a long tradition. Several sets of test problems have been developed and new problems are still collected. So, a whole variety of problems can be used to check the eeciency of a method under investigation. In general, eeciency is measured by the amount of work which is necessary to get a reliable solution for a prescribed accuracy. In order to quantify the term \amount of work" usually not only the computing time is measured but also the number of calls of functional units. To quantify the term \quality of a numerical solution" usually the l2 {norm of the true error at the nal point of the integration interval is used. In our contribution we rst discuss some general aspects of benchmarking. Then we present a new test frame which allows to solve typical benchmark problems with some of the state of the art integrators within a uniied framework. Finally we show some results of our benchmark tests. Part of the test frame can be used interactively in the World Wide Web.