EXPLICIT EXPONENTIAL METHOD FOR THE INTEGRATION OF STIFF ORDINARY DIFFERENTIAL-EQUATIONS

A new procedure for the integration of both stiff and nonstiff ordinary differential equations is presented. This new approach, which is applicable to general nonlinear systems, is fully explicit, requires little computer memory, and is very easy to program. It does not require computation of a Jacobian matrix or the solution of algebraic equations. The new algorithm has much better stability properties than the classical explicit methods and is generally much more efficient than these methods for stiff problems. The new approach automatically partitions the dependent variables at every step into stiff and nonstiff groups, and subsequently integrates each accordingly, using a nonstiff method for the nonstiff variables and a new explicit exponential method for the stiff variables. The algorithm blends these approximations appropriately. Because of the automatic partitioning, the new algorithm is entirely suitable for both stiff and nonstiff problems.