Construction of a web-based library for testing the performance of numerical software for ODEs

The development, of an Ordinary Differential Equation (ODE) solver test library presents several challenges, as there is no accepted technique to verify the correctness of the solution obtained by a particular solver. A comparison of results obtained by different algorithms is also difficult due to the differences in the reporting intervals. In this paper we show that solving an ODE with both stiff and non-stiff algorithms can provide a validation to the correctness of the solution. The results obtained by different algorithms can be compared based on initial, minimal, maximal and final values of the differential variables. Cubic spline interpolation can be used to compare integrated values at equal intervals. In the example presented, the need and the potential benefits of an ODE test library are demonstrated. It is shown that even a widely used and well tested algorithm may yield incorrect or even absurd results under certain circumstances.