Performance assessment of exponential Rosenbrock methods for large systems of ODEs

Elliot Joseph Carr, Timothy John Moroney, Ian William Turner


This article studies time integration methods for stiff systems of ordinary differential equations of large dimension. For such problems, implicit methods generally outperform explicit methods because the step size is usually less restricted by stability constraints. Recently, however, a family of explicit methods, called exponential integrators, have become popular for large stiff problems due to their favourable stability properties and the rapid convergence of non-preconditioned Krylov subspace methods for computing matrix-vector products involving exponential-like functions of the Jacobian matrix. In this article, we implement the so-called exponential Rosenbrock methods using Krylov subspaces. Numerical experiments on a challenging real-world test problem reveal that these methods are a promising preconditioner-free alternative to well-established approaches based on preconditioned Newton--Krylov implementations of the backward differentiation formulas.

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exponential integrators, backward differentiation formulas, stiff ODEs, Krylov subspace methods, porous media

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