Can i trust this software package? An exercise in validation of computational results

A systematic approach for identification of causes for a failure in an ODE integration algorithm used to reach a correct solution of a particular problem is presented. The procedure checks that whether a similar algorithm in a different package yields the same solution and whether the default algorithm parameters are appropriate. The stiffness of the problem is assessed and a comparison of solutions obtained by stiff and non-stiff algorithms was carried out. Numerical software was used to solve ODEs and demonstrated that the results of ODE solvers must be verified and the reduction of error tolerances and problem solution by different packages are very efficient in detecting accurate solutions. The Polymath package was found to be most suitable for such tests as it enabled the export of model equations to other packages and can be used when difficulties are encountered during numerical problem solving.