Communications on Applied Mathematics and Computation >

2021 , Vol. 3 >Issue 4: 719 - 758

DOI: https://doi.org/10.1007/s42967-021-00158-x

ORIGINAL PAPER

Strong Stability Preserving IMEX Methods for Partitioned Systems of Diferential Equations

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  • 1 Member of the INdAM Research group GNCS, Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Università degli Studi di Napoli Federico Ⅱ, 80126 Napoli, Italy;
    2 School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA;
    3 Faculty of Applied Mathematics, AGH University of Science and Technology, Kraków, Poland

Received date: 2021-05-09

  Revised date: 2021-07-11

  Online published: 2021-11-25

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Abstract

We investigate strong stability preserving (SSP) implicit-explicit (IMEX) methods for partitioned systems of diferential equations with stif and nonstif subsystems. Conditions for order p and stage order q = p are derived, and characterization of SSP IMEX methods is provided following the recent work by Spijker. Stability properties of these methods with respect to the decoupled linear system with a complex parameter, and a coupled linear system with real parameters are also investigated. Examples of methods up to the order p = 4 and stage order q = p are provided. Numerical examples on six partitioned test systems confrm that the derived methods achieve the expected order of convergence for large range of stepsizes of integration, and they are also suitable for preserving the accuracy in the stif limit or preserving the positivity of the numerical solution for large stepsizes.

Key words： Partitioned systems of diferential equations; SSP property; IMEX general linear methods; Construction of highly stable methods

Cite this article

Giuseppe Izzo, Zdzisław Jackiewicz . Strong Stability Preserving IMEX Methods for Partitioned Systems of Diferential Equations[J]. Communications on Applied Mathematics and Computation, 2021 , 3(4) : 719 -758 . DOI: 10.1007/s42967-021-00158-x

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