Transformed implicit-explicit DIMSIMs with strong stability preserving explicit part

Research output: Contribution to journalArticle

Abstract

For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stiff or mildly stiff, and the other part is stiff. Such systems can be efficiently treated by a class of implicit-explicit (IMEX) diagonally implicit multistage integration methods (DIMSIMs), where the stiff part is integrated by an implicit formula, and the non-stiff part is integrated by an explicit formula. We will construct methods where the explicit part has strong stability preserving (SSP) property, and the implicit part of the method is A-, or L-stable. We will also investigate stability of these methods when the implicit and explicit parts interact with each other. To be more precise, we will monitor the size of the region of absolute stability of the IMEX scheme, assuming that the implicit part of the method is A-, or L-stable. Finally, we furnish examples of SSP IMEX DIMSIMs up to the order four with good stability properties.

Original languageEnglish (US)
JournalNumerical Algorithms
DOIs
StateAccepted/In press - Jan 1 2019

Fingerprint

Strong Stability
Differential equations
Absolute Stability
Explicit Scheme
Implicit Scheme
System of Differential Equations
Explicit Formula
Monitor
Engineering

Keywords

  • Construction of highly stable methods
  • DIMSIMs
  • General linear methods
  • IMEX methods
  • SSP property
  • Stability analysis

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

@article{84b95715a62444a4b03b75a512b2a29d,
title = "Transformed implicit-explicit DIMSIMs with strong stability preserving explicit part",
abstract = "For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stiff or mildly stiff, and the other part is stiff. Such systems can be efficiently treated by a class of implicit-explicit (IMEX) diagonally implicit multistage integration methods (DIMSIMs), where the stiff part is integrated by an implicit formula, and the non-stiff part is integrated by an explicit formula. We will construct methods where the explicit part has strong stability preserving (SSP) property, and the implicit part of the method is A-, or L-stable. We will also investigate stability of these methods when the implicit and explicit parts interact with each other. To be more precise, we will monitor the size of the region of absolute stability of the IMEX scheme, assuming that the implicit part of the method is A-, or L-stable. Finally, we furnish examples of SSP IMEX DIMSIMs up to the order four with good stability properties.",
keywords = "Construction of highly stable methods, DIMSIMs, General linear methods, IMEX methods, SSP property, Stability analysis",
author = "G. Izzo and Zdzislaw Jackiewicz",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/s11075-018-0647-3",
language = "English (US)",
journal = "Numerical Algorithms",
issn = "1017-1398",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Transformed implicit-explicit DIMSIMs with strong stability preserving explicit part

AU - Izzo, G.

AU - Jackiewicz, Zdzislaw

PY - 2019/1/1

Y1 - 2019/1/1

N2 - For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stiff or mildly stiff, and the other part is stiff. Such systems can be efficiently treated by a class of implicit-explicit (IMEX) diagonally implicit multistage integration methods (DIMSIMs), where the stiff part is integrated by an implicit formula, and the non-stiff part is integrated by an explicit formula. We will construct methods where the explicit part has strong stability preserving (SSP) property, and the implicit part of the method is A-, or L-stable. We will also investigate stability of these methods when the implicit and explicit parts interact with each other. To be more precise, we will monitor the size of the region of absolute stability of the IMEX scheme, assuming that the implicit part of the method is A-, or L-stable. Finally, we furnish examples of SSP IMEX DIMSIMs up to the order four with good stability properties.

AB - For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stiff or mildly stiff, and the other part is stiff. Such systems can be efficiently treated by a class of implicit-explicit (IMEX) diagonally implicit multistage integration methods (DIMSIMs), where the stiff part is integrated by an implicit formula, and the non-stiff part is integrated by an explicit formula. We will construct methods where the explicit part has strong stability preserving (SSP) property, and the implicit part of the method is A-, or L-stable. We will also investigate stability of these methods when the implicit and explicit parts interact with each other. To be more precise, we will monitor the size of the region of absolute stability of the IMEX scheme, assuming that the implicit part of the method is A-, or L-stable. Finally, we furnish examples of SSP IMEX DIMSIMs up to the order four with good stability properties.

KW - Construction of highly stable methods

KW - DIMSIMs

KW - General linear methods

KW - IMEX methods

KW - SSP property

KW - Stability analysis

UR - http://www.scopus.com/inward/record.url?scp=85059586849&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85059586849&partnerID=8YFLogxK

U2 - 10.1007/s11075-018-0647-3

DO - 10.1007/s11075-018-0647-3

M3 - Article

AN - SCOPUS:85059586849

JO - Numerical Algorithms

JF - Numerical Algorithms

SN - 1017-1398

ER -