A second-order Magnus-type integrator for nonautonomous parabolic problems

Authors:
C. González;A. Ostermann;M. Thalhammer
Affiliations:
Departamento de Matemática Aplicada y Computación, Universidad de Valladolid, E-47011 Valladolid, Spain;Institut für Mathematik, Universität Innsbruck, Technikerstraíe 25, A-6020 Innsbruck, Austria;Institut für Mathematik, Universität Innsbruck, Technikerstraíe 25, A-6020 Innsbruck, Austria
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

We analyse stability and convergence properties of a second-order Magnus-type integrator for linear parabolic differential equations with time-dependent coefficients, working in an analytic framework of sectorial operators in Banach spaces. Under reasonable smoothness assumptions on the data and the exact solution, we prove a second-order convergence result without unnatural restrictions on the time stepsize. However, if the error is measured in the domain of the differential operator, an order reduction occurs, in general. A numerical example illustrates and confirms our theoretical results.