Volume 41, pp. 497-511, 2014.

An exponential integrator for non-autonomous parabolic problems

David Hipp, Marlis Hochbruck, and Alexander Ostermann

Abstract

For the time integration of non-autonomous parabolic problems, a new type of exponential integrators is presented and analyzed. The construction of this integrator is closely related to general construction principles of the continuous evolution system. The proximity to the continuous problem allows one to obtain a third-order method that does not suffer from order reduction. The stated order behavior is rigorously proved in an abstract framework of analytic semigroups. The numerical behavior of the integrator is illustrated with an example that models a diffusion process on an evolving domain. Comparisons with an implicit Runge-Kutta method of order three and a standard fourth-order Magnus integrator are given.

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Key words

exponential integrators, parabolic problems, time-dependent operators, evolving domains

AMS subject classifications

65M12, 65L06

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