TY - GEN A1 - Deuflhard, Peter T1 - Adaptive Pseudo-transient Continuation for Nonlinear Steady State Problems N2 - Pseudo--transient continuation methods are quite popular for the numerical solution of steady state problems, typically in PDEs. They are based on an embedding into a time dependent initial value problem. In the presence of dynamical invariants the Jacobian matrix of the nonlinear equation system is bound to be singular. The paper presents a convergence analysis which takes this property into account -- in contrast to known approaches. On the basis of the new analysis adaptive algorithms are suggested in detail. These include a variant with Jacobian approximations as well as inexact pseudo--transient continuation, both of which play an important role in discretized PDEs. Numerical experiments are left to future work. T3 - ZIB-Report - 02-14 KW - pseudo--transient continuation KW - linearly implicit KW - Euler discretization KW - stiff integration KW - contractivity of ordinary differential equations KW - lar Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6814 ER -