Error analysis of multirate leapfrog-type methods for second-order semilinear ODEs
Year: 2021
Type: book
Abstract: In this paper we consider the numerical solution of second-order semilinear differential equations, for which the stiffness is induced by only a few components of the linear part. For such problems, the leapfrog scheme suffers from severe restrictions on the step size to ensure stability. We thus propose a general class of multirate leapfrog-type methods which allows to use step sizes which are independent on the stiff part of the equation and also very efficient to implement. This class comprises local time-stepping schemes [5, 7] but also locally implicit or locally trigonometric integrators. Our main contribution is a rigorous error and stability analysis with special emphasis on explicit multirate methods, which are based on stabilized leapfrog-Chebyshev polynomials introduced in [4].
Authors: Carle, Constantin, Hochbruck, Marlis
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W3195871935