Removal of contrived chaos in finite-difference methods

A. B. Gumel

doi:10.1080/00207160212120

Removal of contrived chaos in finite-difference methods

A. B. Gumel

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

4 Scopus citations

Abstract

A chaos-free numerical method will be developed for the solution of a system of non-linear initial-value problems (IVP's) associated with the transmission dynamics of two HIV subtypes. It will be shown that integration of this four-dimensional system with some standard numerical integrators like the fourth-order Runge-Kutta algorithm leads to scheme-dependent numerical instabilities.

Original language	English (US)
Pages (from-to)	1033-1041
Number of pages	9
Journal	International Journal of Computer Mathematics
Volume	79
Issue number	9
DOIs	https://doi.org/10.1080/00207160212120
State	Published - 2002
Externally published	Yes

Keywords

Chaos
Finite-difference method
Initial-value problem
Stability

ASJC Scopus subject areas

Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

Access to Document

10.1080/00207160212120

Cite this

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title = "Removal of contrived chaos in finite-difference methods",

abstract = "A chaos-free numerical method will be developed for the solution of a system of non-linear initial-value problems (IVP's) associated with the transmission dynamics of two HIV subtypes. It will be shown that integration of this four-dimensional system with some standard numerical integrators like the fourth-order Runge-Kutta algorithm leads to scheme-dependent numerical instabilities.",

keywords = "Chaos, Finite-difference method, Initial-value problem, Stability",

author = "Gumel, {A. B.}",

note = "Funding Information: The author acknowledges, with thanks, the support of the Natural Sciences and Engineering Research Council of Canada (NSERC). The author is very grateful to Prof. R.E. Mickens (Clark Atlanta University, USA) for his useful comments. The author is also grateful to the reviewer for his/her comments which have improved the paper.",

year = "2002",

doi = "10.1080/00207160212120",

language = "English (US)",

volume = "79",

pages = "1033--1041",

journal = "International Journal of Computer Mathematics",

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T1 - Removal of contrived chaos in finite-difference methods

AU - Gumel, A. B.

N1 - Funding Information: The author acknowledges, with thanks, the support of the Natural Sciences and Engineering Research Council of Canada (NSERC). The author is very grateful to Prof. R.E. Mickens (Clark Atlanta University, USA) for his useful comments. The author is also grateful to the reviewer for his/her comments which have improved the paper.

PY - 2002

Y1 - 2002

N2 - A chaos-free numerical method will be developed for the solution of a system of non-linear initial-value problems (IVP's) associated with the transmission dynamics of two HIV subtypes. It will be shown that integration of this four-dimensional system with some standard numerical integrators like the fourth-order Runge-Kutta algorithm leads to scheme-dependent numerical instabilities.

AB - A chaos-free numerical method will be developed for the solution of a system of non-linear initial-value problems (IVP's) associated with the transmission dynamics of two HIV subtypes. It will be shown that integration of this four-dimensional system with some standard numerical integrators like the fourth-order Runge-Kutta algorithm leads to scheme-dependent numerical instabilities.

KW - Chaos

KW - Finite-difference method

KW - Initial-value problem

KW - Stability

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DO - 10.1080/00207160212120

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EP - 1041

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

IS - 9

ER -

Removal of contrived chaos in finite-difference methods

Abstract

Keywords

ASJC Scopus subject areas

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