Pseudo-Transient Continuation Applied to Differential-Algebraic Equations

Todd S. Coffey

Center for Research in Scientific Computing
Mathematics Department, Box 8205
North Carolina State University
Raleigh, NC 27695-8205, USA


C. T. Kelley
Center for Research in Scientific Computation
Department of Mathematics, Box 8205
North Carolina State University
Raleigh, NC 27695-8205, USA


David E. Keyes
Department of Mathematics and Statistics
Old Dominion University
Norfolk, VA 23529-0077


Abstract

Pseudo-transient continuation is a numerical method for computing steady-state solutions of partial differential equations. The existing theory for this method includes a global convergence result for discretized PDEs written as ordinary differential equations. Many problems are better formulated or can only be formulated as partial differential-algebraic equations. In this talk we discuss a global convergence result for pseudo-transient continuation applied to semi-explicit index-1 DAEs and illustrate it with a numerical example.

Key words: pseudo-transient continuation, nonlinear equations, steady state solutions, global convergence, differential-algebraic equations, semi-explicit

AMS subject classifications. 65H10, 65J15, 65L80, 65N12, 65N22