Exploiting structure in the construction of DIMSIMs

Zdzislaw Jackiewicz; Hans Mittelmann

doi:10.1016/S0377-0427(99)00091-6

Exploiting structure in the construction of DIMSIMs

Zdzislaw Jackiewicz, Hans Mittelmann

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We describe the structure of the nonlinear system for the coefficients of diagonally implicit multistage integration methods for ordinary differential equations. This structure is then utilized in the search for methods of high order and stage order with a given stability function. New methods were obtained by solving the nonlinear systems by state-of-the-art software based on least squares minimization.

Original language	English (US)
Pages (from-to)	233-239
Number of pages	7
Journal	Journal of Computational and Applied Mathematics
Volume	107
Issue number	2
DOIs	https://doi.org/10.1016/S0377-0427(99)00091-6
State	Published - Jul 31 1999

Keywords

65L05
65L20
A-stability
General linear method
Least-squares minimization
Ordinary differential equation

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/S0377-0427(99)00091-6

Cite this

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title = "Exploiting structure in the construction of DIMSIMs",

abstract = "We describe the structure of the nonlinear system for the coefficients of diagonally implicit multistage integration methods for ordinary differential equations. This structure is then utilized in the search for methods of high order and stage order with a given stability function. New methods were obtained by solving the nonlinear systems by state-of-the-art software based on least squares minimization.",

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AU - Jackiewicz, Zdzislaw

AU - Mittelmann, Hans

PY - 1999/7/31

Y1 - 1999/7/31

N2 - We describe the structure of the nonlinear system for the coefficients of diagonally implicit multistage integration methods for ordinary differential equations. This structure is then utilized in the search for methods of high order and stage order with a given stability function. New methods were obtained by solving the nonlinear systems by state-of-the-art software based on least squares minimization.

AB - We describe the structure of the nonlinear system for the coefficients of diagonally implicit multistage integration methods for ordinary differential equations. This structure is then utilized in the search for methods of high order and stage order with a given stability function. New methods were obtained by solving the nonlinear systems by state-of-the-art software based on least squares minimization.

KW - 65L05

KW - 65L20

KW - A-stability

KW - General linear method

KW - Least-squares minimization

KW - Ordinary differential equation

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DO - 10.1016/S0377-0427(99)00091-6

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EP - 239

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

Exploiting structure in the construction of DIMSIMs

Abstract

Keywords

ASJC Scopus subject areas

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