Adaptive Numerical Methods With Arbitrary Fixed Samplings

Abstract

The weak stability of linear multistep methods for real-time simulation of systems leads to the design of a class of linear multistep methods with varying coefficients. These methods do not suffer from weak instability and are generally very useful, especially for real-time simulation of stiff nonlinear systems. This paper presents an adaptive technique for numerical integration that allows the simulation stepsize to be chosen independently of the system eigenvalues. The method tracks most changes in the dynamics of the system and changes accordingly the integration coefficients to ensure accuracy and stability of the simulation.