Strong Stability Preserving IMEX Methods for Partitioned Systems of Diferential Equations

doi:10.1007/s42967-021-00158-x

Communications on Applied Mathematics and Computation ›› 2021, Vol. 3 ›› Issue (4): 719-758.doi: 10.1007/s42967-021-00158-x

• ORIGINAL PAPERS • 上一篇

Strong Stability Preserving IMEX Methods for Partitioned Systems of Diferential Equations

Giuseppe Izzo¹, Zdzisław Jackiewicz^2,3

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

收稿日期:2021-05-09 修回日期:2021-07-11 出版日期:2021-11-20 发布日期:2021-11-25
通讯作者: Giuseppe Izzo, Zdzisław Jackiewicz E-mail:giuseppe.izzo@unina.it;jackiewicz@asu.edu

Strong Stability Preserving IMEX Methods for Partitioned Systems of Diferential Equations

Giuseppe Izzo¹, Zdzisław Jackiewicz^2,3

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:2021-05-09 Revised:2021-07-11 Online:2021-11-20 Published:2021-11-25
Contact: Giuseppe Izzo, Zdzisław Jackiewicz E-mail:giuseppe.izzo@unina.it;jackiewicz@asu.edu

摘要/Abstract

摘要： 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.

关键词: Partitioned systems of diferential equations, SSP property, IMEX general linear methods, Construction of highly stable methods

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

中图分类号:

65L05

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.

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Strong Stability Preserving IMEX Methods for Partitioned Systems of Diferential Equations

Strong Stability Preserving IMEX Methods for Partitioned Systems of Diferential Equations

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