Auto Validating Methods in Dynamical Systems

Cornell University, Ithaca NY

Investigators

Abstract

Tucker 0107242 The investigator studies the effects of errors imposed by numerical computations carried out in most applied environments (e.g. commercial computers). He focuses on rigorous control of errors in the numerical solution of systems of ordinary differential equations, particularly chaotic dynamical systems. The goal is to provide accurate estimates of the errors of the actual calculations, and to introduce an accurate means of dealing with rounding/truncation errors. Auto-validating methods for the numerical solution of mathematical problems or of mathematical models of science and engineering problems, especially chaotic dynamical systems, is becoming increasingly important. Rigorous error estimates, valuable for any computational model, are especially important in chaotic systems, which arise in modeling weather, neural networks, and so on. The investigator