Numerically Stable Explicit Integration Techniques Using a Linearized Runge Kutta Extension

摘要

Computer aided design requires repeated evaluation of the performance of a system model during development of the model and during parameter optimization. The analysis of a differential system model thus requires an efficient solution of a set of nonlinear ordinary differential equations, x dot = f(x,t), that model the system. Accurate system models contain short and long term effects; therefore such models have wide ranges of time constants (eigenvalues). Most numerical integration rules, including the Runge Kutta rules, require for numerical stability of the calculated response that the integration time step be limited by the smallest and possibly most uninteresting time constant. Some implicit integration rules, which require iteration, have no numerical instabilities regardless of the time step size. Presented in this paper is an investigation of a class of explicit integration rules, requiring no iteration, that possess numerical stability for any integration time step. Integration rules do not require limitation of the integration time step to provide numerical stability can reduce the number of integration steps significantly and thus greatly decrease the computer execution time necessary to calculate the response. (Author)