Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Runge-Kutta approximation of quasi-linear parabolic equations

Authors: Christian Lubich and Alexander Ostermann
Journal: Math. Comp. 64 (1995), 601-627
MSC: Primary 65M12; Secondary 65J15, 65M20
MathSciNet review: 1284670
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study the convergence properties of implicit Runge-Kutta methods applied to time discretization of parabolic equations with time- or solution-dependent operator. Error bounds are derived in the energy norm. The convergence analysis uses two different approaches. The first, technically simpler approach relies on energy estimates and requires algebraic stability of the Runge-Kutta method. The second one is based on estimates for linear time-invariant equations and uses Fourier and perturbation techniques. It applies to $ A(\theta )$-stable Runge-Kutta methods and yields the precise temporal order of convergence. This order is noninteger in general and depends on the type of boundary conditions.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65M12, 65J15, 65M20

Retrieve articles in all journals with MSC: 65M12, 65J15, 65M20

Additional Information

Keywords: Runge-Kutta time discretization, quasi-linear parabolic equations, error bounds, algebraic stability, $ A(\theta )$-stability
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society