Search for highly stable two-step Runge-Kutta methods

R. D'Ambrosio; G. Izzo; Zdzislaw Jackiewicz

doi:10.1016/j.apnum.2012.06.012

Search for highly stable two-step Runge-Kutta methods

R. D'Ambrosio, G. Izzo, Zdzislaw Jackiewicz

Mathematical and Statistical Sciences, School of (SoMSS)

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

29 Scopus citations

Abstract

We describe the search for A-stable and algebraically stable two-step Runge Kutta methods of order p and stage order q=p or q=p-1. The search for A-stable methods is based on the Schur criterion applied for specific methods with stability polynomial of reduced degree. The search for algebraically stable methods is based on the criteria proposed recently by Hewitt and Hill.

Original language	English (US)
Pages (from-to)	1361-1379
Number of pages	19
Journal	Applied Numerical Mathematics
Volume	62
Issue number	10
DOIs	https://doi.org/10.1016/j.apnum.2012.06.012
State	Published - Oct 2012

Keywords

A-stability
Algebraic stability
Linear stability analysis
Order conditions
Two-step Runge-Kutta methods

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1016/j.apnum.2012.06.012

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title = "Search for highly stable two-step Runge-Kutta methods",

abstract = "We describe the search for A-stable and algebraically stable two-step Runge Kutta methods of order p and stage order q=p or q=p-1. The search for A-stable methods is based on the Schur criterion applied for specific methods with stability polynomial of reduced degree. The search for algebraically stable methods is based on the criteria proposed recently by Hewitt and Hill.",

keywords = "A-stability, Algebraic stability, Linear stability analysis, Order conditions, Two-step Runge-Kutta methods",

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

note = "Funding Information: E-mail addresses: rdambrosio@unisa.it (R. D{\textquoteright}Ambrosio), giuseppe.izzo@unina.it (G. Izzo), jackiewi@math.la.asu.edu (Z. Jackiewicz). 1 Partially supported by the Gruppo Nazionale per il Calcolo Scientifico. 2 Partially supported by the National Science Foundation under grant NSF DMS-0510813, by DMA “R. Caccioppoli” – Universit{\`a} di Napoli “Federico II” and by DMI – Universit{\`a} di Salerno.",

year = "2012",

month = oct,

doi = "10.1016/j.apnum.2012.06.012",

language = "English (US)",

volume = "62",

pages = "1361--1379",

journal = "Applied Numerical Mathematics",

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AU - Izzo, G.

AU - Jackiewicz, Zdzislaw

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PY - 2012/10

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N2 - We describe the search for A-stable and algebraically stable two-step Runge Kutta methods of order p and stage order q=p or q=p-1. The search for A-stable methods is based on the Schur criterion applied for specific methods with stability polynomial of reduced degree. The search for algebraically stable methods is based on the criteria proposed recently by Hewitt and Hill.

AB - We describe the search for A-stable and algebraically stable two-step Runge Kutta methods of order p and stage order q=p or q=p-1. The search for A-stable methods is based on the Schur criterion applied for specific methods with stability polynomial of reduced degree. The search for algebraically stable methods is based on the criteria proposed recently by Hewitt and Hill.

KW - A-stability

KW - Algebraic stability

KW - Linear stability analysis

KW - Order conditions

KW - Two-step Runge-Kutta methods

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JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

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ER -

Search for highly stable two-step Runge-Kutta methods

Abstract

Keywords

ASJC Scopus subject areas

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