Performance assessment of exponential Rosenbrock methods for large systems of ODEs


  • Elliot Joseph Carr Queensland University of Technology
  • Timothy John Moroney Queensland University of Technology
  • Ian William Turner Queensland University of Technology



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


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. References
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