Error Analysis in the Computer Simulation of Dynamic Systems: Variational Aspects of the Problem

Abstract

Error analysis in the computer simulation of dynamic systems is fundamentally a variational problem. The computing errors are small variations of the computed solutions with respect to the exact solution of the differential equations being integrated. It is not surprising, therefore, that many of the mathematical tools used to perform error analysis in the computer simulation of dynamic systems are similar to those used in the variational or perturbational analysis of those systems themselves. Fundamental papers in this direction have been published previously [8], [9], [13]. The present paper, however derives the error-propagation equations in a more basic form, which makes it easier to apply such variational mathematical tools as Liapunoff's second method to analyze error stability, and Pontryagin's maximum principle to study ``worst-case'' errors in computation.