Year: 1993
Type: article
Abstract: 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 Runge-Kutta methods as convolution quadratures. In a different context, these can be used as efficient computational methods for the approximation of convolution integrals and integral equations. They use the Laplace transform of the convolution kernel via a discrete operational calculus.
Source: Mathematics of Computation
Authors: Ch. Lubich, A. Ostermann
Institutions: ETH Zurich, Seminar for Applied Mathematics
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2017611864