Two-step almost collocation methods for ordinary differential equations

R. D'Ambrosio; M. Ferro; Zdzislaw Jackiewicz; B. Paternoster

doi:10.1007/s11075-009-9280-5

Two-step almost collocation methods for ordinary differential equations

R. D'Ambrosio, M. Ferro, Zdzislaw Jackiewicz, B. Paternoster

Mathematical and Statistical Sciences, School of (SoMSS)

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

42 Scopus citations

Abstract

A new class of two-step Runge-Kutta methods for the numerical solution of ordinary differential equations is proposed. These methods are obtained using the collocation approach by relaxing some of the collocation conditions to obtain methods with desirable stability properties. Local error estimation for these methods is also discussed.

Original language	English (US)
Pages (from-to)	195-217
Number of pages	23
Journal	Numerical Algorithms
Volume	53
Issue number	2-3
DOIs	https://doi.org/10.1007/s11075-009-9280-5
State	Published - Jan 2010

Keywords

A-stability
Absolute stability
Local error estimation
Order conditions
Two-step collocation methods

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s11075-009-9280-5

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title = "Two-step almost collocation methods for ordinary differential equations",

abstract = "A new class of two-step Runge-Kutta methods for the numerical solution of ordinary differential equations is proposed. These methods are obtained using the collocation approach by relaxing some of the collocation conditions to obtain methods with desirable stability properties. Local error estimation for these methods is also discussed.",

keywords = "A-stability, Absolute stability, Local error estimation, Order conditions, Two-step collocation methods",

author = "R. D'Ambrosio and M. Ferro and Zdzislaw Jackiewicz and B. Paternoster",

note = "Funding Information: The work of the third author was partially supported by the National Science Foundation under grant NSF DMS–0510813 and by Consiglio Nazionale delle Ricerche.",

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doi = "10.1007/s11075-009-9280-5",

language = "English (US)",

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AU - D'Ambrosio, R.

AU - Ferro, M.

AU - Jackiewicz, Zdzislaw

AU - Paternoster, B.

N1 - Funding Information: The work of the third author was partially supported by the National Science Foundation under grant NSF DMS–0510813 and by Consiglio Nazionale delle Ricerche.

PY - 2010/1

Y1 - 2010/1

N2 - A new class of two-step Runge-Kutta methods for the numerical solution of ordinary differential equations is proposed. These methods are obtained using the collocation approach by relaxing some of the collocation conditions to obtain methods with desirable stability properties. Local error estimation for these methods is also discussed.

AB - A new class of two-step Runge-Kutta methods for the numerical solution of ordinary differential equations is proposed. These methods are obtained using the collocation approach by relaxing some of the collocation conditions to obtain methods with desirable stability properties. Local error estimation for these methods is also discussed.

KW - A-stability

KW - Absolute stability

KW - Local error estimation

KW - Order conditions

KW - Two-step collocation methods

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ER -

Two-step almost collocation methods for ordinary differential equations

Abstract

Keywords

ASJC Scopus subject areas

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