![]() ![]() Relative behavior is predicted ''on the average'' and applied to assessing the quality of Runge-Kutta formulas and their error estimators. ![]() Confronted with the fact that changing the form more ยป of an equation without altering its solution can reverse the relative efficiency of two Runge-Kutta formulas, how can one decide which formula to use. Unfortunately, this is not realistic for codes based on Runge-Kutta methods. ![]() The value of such comparisons hinges on the hypothesis that the performance in nearly all respects depends only on the behavior of the solutions, not the form of the equations themselves. In the case of codes to solve the initial-value problem for ordinary differential equations, the usual procedure is to compare performance on a set of test problems. Critical evaluation of mathematical software is essential for the designation of items worthy of general acceptance and for the production of improved software. ![]()
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