Document Type

Article

Rights

This item is available under a Creative Commons License for non-commercial use only

Disciplines

Applied mathematics

Publication Details

Journal of Computational Physics

Submitted February 12, 2015

Accepted July 22, 2015

© 2015, Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/ licenses/by-nc-nd/4.0/

doi: 10. 1016/ j. jcp. 2015. 07. 050

Abstract

The analytic form of a new class of factorized Runge-Kutta-Chebyshev (FRKC) stability polynomials of arbitrary order N is presented. Roots of FRKC stability polynomials of degree L = MN are used to construct explicit schemes comprising L forward Euler stages with internal stability ensured through a sequencing algorithm which limits the internal amplification factors to ~ L2. The associated stability domain scales as M2 along the real axis. Marginally stable real-valued points on the interior of the stability domain are removed via a prescribed damping procedure. By construction, FRKC schemes meet all linear order conditions; for nonlinear problems at orders above 2, complex splitting or Butcher group composition methods are required. Linear order conditions of the FRKC stability polynomials are verified at orders 2, 4, and 6 in numerical experiments. Comparative studies with existing methods show the second-order unsplit FRKC2 scheme and higher order (4 and 6) split FRKC schemes are efficient for large moderately stiff problems.

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