Runge-Kutta methods for parabolic equations and convolution quadrature
نویسندگان
چکیده
منابع مشابه
Runge-kutta Methods for Parabolic Equations and Convolution Quadrature
We study the approximation properties of Runge-Kutta time discretizations of linear and semilinear parabolic equations, including incompressible Navier-Stokes equations. We derive asymptotically sharp error bounds and relate the temporal order of convergence, which is generally noninteger, to spatial regularity and the type of boundary conditions. The analysis relies on an interpretation of Run...
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Convolution equations for time and space-time problems have many important applications, e.g., for the modelling of wave or heat propagation via ordinary and partial differential equations as well as for the corresponding integral equation formulations. For their discretization, the convolution quadrature (CQ) has been developed since the late 1980’s and is now one of the most popular method in...
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An error analysis of Runge-Kutta convolution quadrature is presented for a class of nonsectorial operators whose Laplace transform satisfies, besides the standard assumptions of analyticity in a half-plane Re s > σ0 and a polynomial bound O(s 1) there, the stronger polynomial bound O(s2) in convex sectors of the form | arg s| ≤ π/2 − θ < π/2 for θ > 0. The order of convergence of the Runge-Kutt...
متن کاملExponential Runge-Kutta methods for parabolic problems
The aim of this paper is to construct exponential Runge-Kutta methods of collocation type and to analyze their convergence properties for linear and semilinear parabolic problems. For the analysis, an abstract Banach space framework of sectorial operators and locally Lipschitz continuous nonlinearities is chosen. This framework includes interesting examples like reaction-diffusion equations. It...
متن کاملAn error analysis of Runge-Kutta convolution quadrature
An error analysis is given for convolution quadratures based on strongly A-stable RungeKutta methods, for the non-sectorial case of a convolution kernel with a Laplace transform that is polynomially bounded in a half-plane. The order of approximation depends on the classical order and stage order of the Runge-Kutta method and on the growth exponent of the Laplace transform. Numerical experiment...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1993
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1993-1153166-7