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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Stiffly accurate Runge–Kutta methods for nonlinear evolution problems governed by a monotone operator
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by Etienne Emmrich and Mechthild Thalhammer PDF
Math. Comp. 79 (2010), 785-806 Request permission

Abstract:

Stiffly accurate implicit Runge–Kutta methods are studied for the time discretisation of nonlinear first-order evolution equations. The equation is supposed to be governed by a time-dependent hemicontinuous operator that is (up to a shift) monotone and coercive, and fulfills a certain growth condition. It is proven that the piecewise constant as well as the piecewise linear interpolant of the time-discrete solution converges towards the exact weak solution, provided the Runge–Kutta method is consistent and satisfies a stability criterion that implies algebraic stability; examples are the Radau IIA and Lobatto IIIC methods. The convergence analysis is also extended to problems involving a strongly continuous perturbation of the monotone main part.
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Additional Information
  • Etienne Emmrich
  • Affiliation: Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany
  • Email: emmrich@math.tu-berlin.de
  • Mechthild Thalhammer
  • Affiliation: Leopold-Franzens-Universität, Institut für Mathematik, Technikerstraße 13/VII, 6020 Innsbruck, Austria
  • MR Author ID: 661917
  • Email: Mechthild.Thalhammer@uibk.ac.at
  • Received by editor(s): September 19, 2008
  • Received by editor(s) in revised form: April 16, 2009
  • Published electronically: July 23, 2009
  • © Copyright 2009 American Mathematical Society
  • Journal: Math. Comp. 79 (2010), 785-806
  • MSC (2000): Primary 65M12, 65M15, 47J35, 35K55, 47H05
  • DOI: https://doi.org/10.1090/S0025-5718-09-02285-6
  • MathSciNet review: 2600543