Interior estimates for time discretizations of parabolic equations
Copyright policy )Interior estimates for time discretizations of parabolic equations
Die Autoren untersuchen Eigenschaften \(q\)-stufiger Runge-Kutta-Verfahren der Ordnung \(p\) (\(p \geq q + 1\)) zur Zeit-Diskretisierung linearer parabolischer Anfangs-Randwertprobleme: Bei experimentellen Untersuchungen des Verfahrensfehlers zeigt sich bei unglatten Randbedingungen bzw. Rändern ein Ordnungsverlust in den Randgebieten, während in Bereichen des Innengebietes die volle Konvergenzordnung \(p\) erhalten bleibt. Mit dem Beweis des Theorem 3, dem Hauptresultat dieser Arbeit, werden die o.e. experimentellen Beobachtungen auf eine saubere mathematische Grundlage gestellt. Die Beweismethode läßt sich auch auf entsprechende Aussagen für BDF-Verfahren übertragen.
- University of Tübingen Germany
- University of Innsbruck Austria
Method of lines for initial value and initial-boundary value problems involving PDEs, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Runge-Kutta methods, convergence, method of times, order reduction, Initial value problems for second-order parabolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, time discretizations
Method of lines for initial value and initial-boundary value problems involving PDEs, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Runge-Kutta methods, convergence, method of times, order reduction, Initial value problems for second-order parabolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, time discretizations
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