SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

Show full list of Invited Contributions to Minisymposia Show talk context (MS16)


Convergence issues of DAEs with non-constant constraints

L. Jansen

Abstract
Two of the best known DAE solver packages are DASSL and RADAU. While RADAU is based on the Radau IIA method, DASSL uses BDF-methods to solve a DAE. The BDF-methods as well as the Radau IIA method may fail to provide a convergent numerical solution for linear DAEs with time depending constraints. In particular these methods do not converge if applied to the following well known example: $ x_1'+\eta t x_2' + (1+\eta)x_2 &= 0 , x_1 +\eta t x_2 &= e^{-t}, $ with $\eta < -0.5$, [1]. While other prominent methods like Lobatto IIIA share the same convergence problem we present a class of discontinuous collocation methods which overcomes this weakness.

Bibliography
[1] R. Lamour, R. März and C. Tischendorf, Differential Algebraic Equations: A Projector Based Analysis, Springer, 2013.

Organized by         Universidad de Valladolid     IMUVA