Continuous two-step Runge-Kutta methods for ordinary differential equations

Raffaele D'Ambrosio; Zdzislaw Jackiewicz

doi:10.1007/s11075-009-9329-5

Continuous two-step Runge-Kutta methods for ordinary differential equations

Raffaele D'Ambrosio, Zdzislaw Jackiewicz

Mathematical and Statistical Sciences, School of (SoMSS)

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

35 Scopus citations

Abstract

New classes of continuous two-step Runge-Kutta methods for the numerical solution of ordinary differential equations are derived. These methods are developed imposing some interpolation and collocation conditions, in order to obtain desirable stability properties such as A-stability and L-stability. Particular structures of the stability polynomial are also investigated.

Original language	English (US)
Pages (from-to)	169-193
Number of pages	25
Journal	Numerical Algorithms
Volume	54
Issue number	2
DOIs	https://doi.org/10.1007/s11075-009-9329-5
State	Published - Jun 2010

Keywords

A-stability
L-stability
Quadratic stability functions
Runge-Kutta stability
Two-step collocation methods

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s11075-009-9329-5

Cite this

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abstract = "New classes of continuous two-step Runge-Kutta methods for the numerical solution of ordinary differential equations are derived. These methods are developed imposing some interpolation and collocation conditions, in order to obtain desirable stability properties such as A-stability and L-stability. Particular structures of the stability polynomial are also investigated.",

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AB - New classes of continuous two-step Runge-Kutta methods for the numerical solution of ordinary differential equations are derived. These methods are developed imposing some interpolation and collocation conditions, in order to obtain desirable stability properties such as A-stability and L-stability. Particular structures of the stability polynomial are also investigated.

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KW - L-stability

KW - Quadratic stability functions

KW - Runge-Kutta stability

KW - Two-step collocation methods

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Continuous two-step Runge-Kutta methods for ordinary differential equations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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