Automatic recognition of non-stiffness

An outstanding characteristic of mathematical software is assistance provided by the code in recognizing that it is unsuitable for the task posed. A critical decision in the present generation of codes for the numerical solution of the initial value problem for a system of ordinary differential equations (ODEs),(1) y' = f(x, y), a < x < b, y(a) given,is whether the problem is stiff. There are effective programs for the solution of both stiff and non-stiff problems which are, however, grossly inefficient when applied to the wrong type. Unfortunately the user does not have available the information necessary for an accurate decision.