Optimal convergence results for Runge-Kutta discretizations of linear nonautonomous parabolic problems
The convergence properties of implicit Runge-Kutta methods for the time-discretization of linear nonautonomous parabolic problems is analyzed. The authors work in an abstract Banach space setting that covers standard parabolic initial-boundary value problems with time-dependent smooth coefficients. The Runge-Kutta methods are only assumed to be \(A (\theta)\)-stable, and variable stepsizes are allowed in the analysis. As the main result optimal convergence rates for Runge-Kutta discretizations of temporally smooth solutions are derived.
parabolic initial-boundary value problems
scientific article; zbMATH DE number 1275243