Runge-Kutta convolution coercivity and its use for time-dependent boundary integral equations

Lehel Banjai, Christian Lubich

Research output: Contribution to journalArticle

Abstract

A coercivity property of temporal convolution operators is an essential tool in the analysis of time-dependent boundary integral equations and their space and time discretizations. It is known that this coercivity property is inherited by convolution quadrature time discretization based on A-stable multistep methods, which are of order at most 2. Here we study the question as to which Runge–Kutta-based convolution quadrature methods inherit the convolution coercivity property. It is shown that this holds without any restriction for the third-order Radau IIA method, and on permitting a shift in the Laplace domain variable, this holds for all algebraically stable Runge–Kutta methods and hence for methods of arbitrary order. As an illustration the discrete convolution coercivity is used to analyse the stability and convergence properties of the time discretization of a nonlinear boundary integral equation that originates from a nonlinear scattering problem for the linear wave equation. Numerical experiments illustrate the error behaviour of the Runge–Kutta convolution quadrature time discretization.
Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalIMA Journal of Numerical Analysis
Early online date7 Jun 2018
DOIs
Publication statusE-pub ahead of print - 7 Jun 2018

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Coercivity
Runge-Kutta
Boundary Integral Equations
Convolution
Time Discretization
Quadrature
Quadrature Method
Multistep Methods
Convolution Operator
Stability and Convergence
Scattering Problems
Runge-Kutta Methods
Laplace
Convergence Properties
Nonlinear Problem
Wave equation
Linear equation
Numerical Experiment
Restriction
Arbitrary

Cite this

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Runge-Kutta convolution coercivity and its use for time-dependent boundary integral equations. / Banjai, Lehel; Lubich, Christian.

In: IMA Journal of Numerical Analysis, 07.06.2018, p. 1-24.

Research output: Contribution to journalArticle

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