Construction of Multistep Integration Formulas for Simulation Purposes

Abstract—Block-oriented simulation languages are a powerful tool for solving simulation problems. A problem of major importance in simulation, however, is the choice of the integration formula to be employed in the integration block. Users of early simulation languages had no difficulty selecting a formula since these languages provided only a single formula. Advanced languages have a number of formulas available, but leave the choice to the user who does not have much to go by except the good names of the formulas. Difficulties which were encountered in the use of multistep formulas made formulas of the Runge-Kutta type more popular. Experience has shown that they are less critical with respect to stability. However, the computing time for a Runge-Kutta formula is considerably larger and for this reason multistep formulas, which include the predictor- corrector scheme, are still appealing.