Sequential and parallel methods for solving first-order hyperbolic equations

M. A. Arigu; E. H. Twizell; A. B. Gumel

doi:10.1002/(SICI)1099-0887(199609)12:9<557::AID-CNM5>3.0.CO;2-J

Sequential and parallel methods for solving first-order hyperbolic equations

M. A. Arigu, E. H. Twizell, A. B. Gumel

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

2 Scopus citations

Abstract

Techniques for two-time level difference schemes are presented for the numerical solution of first-order hyperbolic partial differential equations. The space derivative is approximated by (i) a low-order, and (ii) a higher-order backward difference replacement, resulting in a system of first-order ordinary differential equations, the solutions of which satisfy recurrence relations. The methods are obtained from the recurrence relations and are tested on three linear problems and one non-linear problem from the literature.

Original language	English (US)
Pages (from-to)	557-568
Number of pages	12
Journal	Communications in Numerical Methods in Engineering
Volume	12
Issue number	9
DOIs	https://doi.org/10.1002/(SICI)1099-0887(199609)12:9<557::AID-CNM5>3.0.CO;2-J
State	Published - Sep 1996
Externally published	Yes

Keywords

Finite-difference methods
Hyperbolic equations
Padé approximants
Sequential and parallel implementation

ASJC Scopus subject areas

Software
Modeling and Simulation
Engineering(all)
Computational Theory and Mathematics
Applied Mathematics

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10.1002/(SICI)1099-0887(199609)12:9<557::AID-CNM5>3.0.CO;2-J

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title = "Sequential and parallel methods for solving first-order hyperbolic equations",

abstract = "Techniques for two-time level difference schemes are presented for the numerical solution of first-order hyperbolic partial differential equations. The space derivative is approximated by (i) a low-order, and (ii) a higher-order backward difference replacement, resulting in a system of first-order ordinary differential equations, the solutions of which satisfy recurrence relations. The methods are obtained from the recurrence relations and are tested on three linear problems and one non-linear problem from the literature.",

keywords = "Finite-difference methods, Hyperbolic equations, Pad{\'e} approximants, Sequential and parallel implementation",

author = "Arigu, {M. A.} and Twizell, {E. H.} and Gumel, {A. B.}",

year = "1996",

month = sep,

doi = "10.1002/(SICI)1099-0887(199609)12:9<557::AID-CNM5>3.0.CO;2-J",

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T1 - Sequential and parallel methods for solving first-order hyperbolic equations

AU - Arigu, M. A.

AU - Twizell, E. H.

AU - Gumel, A. B.

PY - 1996/9

Y1 - 1996/9

N2 - Techniques for two-time level difference schemes are presented for the numerical solution of first-order hyperbolic partial differential equations. The space derivative is approximated by (i) a low-order, and (ii) a higher-order backward difference replacement, resulting in a system of first-order ordinary differential equations, the solutions of which satisfy recurrence relations. The methods are obtained from the recurrence relations and are tested on three linear problems and one non-linear problem from the literature.

AB - Techniques for two-time level difference schemes are presented for the numerical solution of first-order hyperbolic partial differential equations. The space derivative is approximated by (i) a low-order, and (ii) a higher-order backward difference replacement, resulting in a system of first-order ordinary differential equations, the solutions of which satisfy recurrence relations. The methods are obtained from the recurrence relations and are tested on three linear problems and one non-linear problem from the literature.

KW - Finite-difference methods

KW - Hyperbolic equations

KW - Padé approximants

KW - Sequential and parallel implementation

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JO - Communications in Numerical Methods in Engineering

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ER -

Sequential and parallel methods for solving first-order hyperbolic equations

Abstract

Keywords

ASJC Scopus subject areas

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