Physical Sciences and Mathematics Commons^™

A Direct Method For The Inversion Of Physical Systems, Lester Caudill, Herschel Rabitz, Attila Askar

Department of Math & Statistics Faculty Publications

A general algorithm for the direct inversion of data to yield unknown functions entering physical systems is presented. Of particular interest are linear and non-linear dynamical systems. The potential broad applicability of this method is examined in the context of a number of coefficient-recovery problems for partial differential equations. Stability issues are addressed and a stabilization approach, based on inverse asymptotic tracking, is proposed. Numerical examples for a simple illustration are presented, demonstrating the effectiveness of the algorithm.