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Generalized convolution quadrature based on Runge-Kutta methods


Lopez-Fernandez, Maria; Sauter, Stefan A (2016). Generalized convolution quadrature based on Runge-Kutta methods. Numerische Mathematik, 133(4):743-779.

Abstract

In this paper, we develop the Runge-Kutta generalized convolution quadrature with variable time stepping for the numerical solution of convolution equations for time and space-time problems and present the corresponding stability and convergence analysis. For this purpose, some new theoretical tools such as tensorial divided differences, summation by parts with Runge-Kutta differences and a calculus for Runge-Kutta discretizations of generalized convolution operators such as an associativity property will be developed in this paper. Numerical examples will illustrate the stable and efficient behavior of the resulting discretization.

Abstract

In this paper, we develop the Runge-Kutta generalized convolution quadrature with variable time stepping for the numerical solution of convolution equations for time and space-time problems and present the corresponding stability and convergence analysis. For this purpose, some new theoretical tools such as tensorial divided differences, summation by parts with Runge-Kutta differences and a calculus for Runge-Kutta discretizations of generalized convolution operators such as an associativity property will be developed in this paper. Numerical examples will illustrate the stable and efficient behavior of the resulting discretization.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:August 2016
Deposited On:10 Aug 2016 08:09
Last Modified:12 Aug 2016 00:00
Publisher:Springer
ISSN:0029-599X
Publisher DOI:https://doi.org/10.1007/s00211-015-0761-2

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