ABSTRACT
With the availability of the scientific computer, this general requirement for models to be highly simplified was completely circumvented; now large sets of nonlinear ODEs/DAEs/PDEs, in principle, can be integrated numerically. In practice, the coding (programming) of a numerical algorithm to solve a particular ODE/DAE/PDE problem system can appear daunting to the scientist or engineer who has limited knowledge and experience in numerical mathematics, and who wishes primarily to arrive at a useful solution without a major investment of time and effort to learn the details of numerical analysis and programming. Additionally, even if the analyst is willing to make this investment of time and effort, the direction this effort should take is often far from clear. The numerical analysis literature typically conveys the impression that highly specialized methods are reported which can be applied only to very specific problems; just finding one or more candidate numerical algorithms can be a major undertaking, not to mention the effort to code these algorithms, test the code with problems for which independent solutions are available, program the problem of interest, and finally evaluate the numerical solution with respect to criteria such as stability, accuracy, convergence, and consistency.
