Projected implicit Runge-Kutta methods for differential-algebraic boundary value problems

Abstract

Differential-algebraic boundary value problems arise in the modeling of singular optimal control problems and in parameter estimation for singular systems. A new class of numerical methods, projected implicit Runge-Kutta methods, for the solution of index-two Hessenberg differential-algebraic systems is introduced. The new methods appear to be particularly promising for boundary value problems, and overcome many of the difficulties associated with previously defined methods for this class of problems. Some important tools for stability analysis are developed, and the underlying ordinary differential equations are introduced, which enable the understanding of numerical stability behavior for linear systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>