Abstract :
The authors analyze the behavior of formulas for the numerical integration of ordinary differential equations by considering the frequency response of the "integrators" in the system being simulated. This approach will appeal to engineers, particularly those with an analog background, as being a familiar way to consider the departures from ideal performance of the "computing elements" used as building blocks in simulation. The method has the advantage that the quality of different formulas can be compared independently of any particular problem and irrespective of whether the problem is linear or nonlinear. It does not, of course, give directly the errors in the overall solution, merely the errors injected by the integrating components, but the necessary theory for deducing solution errors from component errors is available if needed.
