Convergence of Runge-Kutta methods applied to linear partial differential-algebraic equations

Authors:
K. Debrabant;K. Strehmel
Affiliations:
Darmstadt University of Technology, Department of Mathematics, Darmstadt, Germany;Martin-Luther-Universität Halle-Wittenberg, FB Mathematik and Informatik, Institut für Numerische Mathematik, Postfach, Halle (Saale), Germany
Venue:
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Year:
2005

Citing 3
Cited 0

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
Convergence of Runge-Kutta methods for nonlinear parabolic equations

Applied Numerical Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We apply Runge-Kutta methods to linear partial differential-algebraic equations of the form Aut(t,x) + B(uxx(t,x) + rux(t,x)) + Cu(t,x)=f(t,x), where A, B, C ∈ Rn,n and the matrix A is singular. We prove that under certain conditions the temporal convergence order of the fully discrete scheme depends on the time index of the partial differential-algebraic equation. In particular, fractional orders of convergence in time are encountered. Furthermore we show that the fully discrete scheme suffers an order reduction caused by the boundary conditions. Numerical examples confirm the theoretical results.