Two-step runge-kutta methods with quadratic stability functions

D. Conte; R. D'Ambrosio; Zdzislaw Jackiewicz

doi:10.1007/s10915-010-9378-x

Two-step runge-kutta methods with quadratic stability functions

D. Conte, R. D'Ambrosio, Zdzislaw Jackiewicz

Mathematical and Statistical Sciences, School of (SoMSS)

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

29 Scopus citations

Abstract

We describe the construction of implicit two-step Runge-Kutta methods with stability properties determined by quadratic stability functions.We will aim for methods which are A-stable and L-stable and such that the coefficients matrix has a one point spectrum. Examples of methods of order up to eight are provided.

Original language	English (US)
Pages (from-to)	191-218
Number of pages	28
Journal	Journal of Scientific Computing
Volume	44
Issue number	2
DOIs	https://doi.org/10.1007/s10915-010-9378-x
State	Published - Aug 2010

Keywords

A-stability
Absolute stability
L-stability
Order conditions
Quadratic stability polynomials
Two-step Runge-Kutta methods

ASJC Scopus subject areas

Software
Theoretical Computer Science
Numerical Analysis
General Engineering
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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10.1007/s10915-010-9378-x

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title = "Two-step runge-kutta methods with quadratic stability functions",

abstract = "We describe the construction of implicit two-step Runge-Kutta methods with stability properties determined by quadratic stability functions.We will aim for methods which are A-stable and L-stable and such that the coefficients matrix has a one point spectrum. Examples of methods of order up to eight are provided.",

keywords = "A-stability, Absolute stability, L-stability, Order conditions, Quadratic stability polynomials, Two-step Runge-Kutta methods",

author = "D. Conte and R. D'Ambrosio and Zdzislaw Jackiewicz",

note = "Funding Information: The work of R. D{\textquoteright}Ambrosio was partially supported by the University of Salerno, according to an exchange agreement for bi-nationally supervised Ph.D. thesis. The work of Z. Jackiewicz was partially supported by the National Science Foundation under grant NSF DMS–0510813.",

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doi = "10.1007/s10915-010-9378-x",

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AU - Conte, D.

AU - D'Ambrosio, R.

AU - Jackiewicz, Zdzislaw

N1 - Funding Information: The work of R. D’Ambrosio was partially supported by the University of Salerno, according to an exchange agreement for bi-nationally supervised Ph.D. thesis. The work of Z. Jackiewicz was partially supported by the National Science Foundation under grant NSF DMS–0510813.

PY - 2010/8

Y1 - 2010/8

N2 - We describe the construction of implicit two-step Runge-Kutta methods with stability properties determined by quadratic stability functions.We will aim for methods which are A-stable and L-stable and such that the coefficients matrix has a one point spectrum. Examples of methods of order up to eight are provided.

AB - We describe the construction of implicit two-step Runge-Kutta methods with stability properties determined by quadratic stability functions.We will aim for methods which are A-stable and L-stable and such that the coefficients matrix has a one point spectrum. Examples of methods of order up to eight are provided.

KW - A-stability

KW - Absolute stability

KW - L-stability

KW - Order conditions

KW - Quadratic stability polynomials

KW - Two-step Runge-Kutta methods

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Two-step runge-kutta methods with quadratic stability functions

Abstract

Keywords

ASJC Scopus subject areas

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