A test problem for numerical schemes for nonlinear hyperbolic equations

S. Abarbanel; M. Goldberg

doi:10.1016/0045-7825(76)90022-0

A test problem for numerical schemes for nonlinear hyperbolic equations

S. Abarbanel
, M. Goldberg

Tel Aviv University
University of California at Los Angeles

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

Abstract

In this note we solve a model problem to test the applicability of numerical schemes for hyperbolic partial differential equations with shock-containing solutions. This test problem was used successfully in [1]in order to compare analytic and numerical solutions. The construction is made possible by considering the development of a jump discontinuity in the solution of scalar quasilinear equations with piecewise smooth data. This is a simple generalization of a discussion by Lax [2].

Original language	English
Pages (from-to)	331-334
Number of pages	4
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	8
Issue number	3
DOIs	https://doi.org/10.1016/0045-7825(76)90022-0
State	Published - 1976
Externally published	Yes

Bibliographical note

Funding Information:
* Sponsored in part by the Air Force Office of Scientific Research (NAM) through the European Office of Aerospace Research, AFSC, United States Air Force, under Grant AFOSR-72-2370.

Funding

* Sponsored in part by the Air Force Office of Scientific Research (NAM) through the European Office of Aerospace Research, AFSC, United States Air Force, under Grant AFOSR-72-2370.

Funders	Funder number
European Office of Aerospace Research
Air Force Office of Scientific Research
U.S. Air Force	AFOSR-72-2370
National Academy of Medicine
Air Force Systems Command

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10.1016/0045-7825(76)90022-0

Cite this

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title = "A test problem for numerical schemes for nonlinear hyperbolic equations",

abstract = "In this note we solve a model problem to test the applicability of numerical schemes for hyperbolic partial differential equations with shock-containing solutions. This test problem was used successfully in [1]in order to compare analytic and numerical solutions. The construction is made possible by considering the development of a jump discontinuity in the solution of scalar quasilinear equations with piecewise smooth data. This is a simple generalization of a discussion by Lax [2].",

author = "S. Abarbanel and M. Goldberg",

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AU - Abarbanel, S.

AU - Goldberg, M.

N1 - Funding Information: * Sponsored in part by the Air Force Office of Scientific Research (NAM) through the European Office of Aerospace Research, AFSC, United States Air Force, under Grant AFOSR-72-2370.

PY - 1976

Y1 - 1976

N2 - In this note we solve a model problem to test the applicability of numerical schemes for hyperbolic partial differential equations with shock-containing solutions. This test problem was used successfully in [1]in order to compare analytic and numerical solutions. The construction is made possible by considering the development of a jump discontinuity in the solution of scalar quasilinear equations with piecewise smooth data. This is a simple generalization of a discussion by Lax [2].

AB - In this note we solve a model problem to test the applicability of numerical schemes for hyperbolic partial differential equations with shock-containing solutions. This test problem was used successfully in [1]in order to compare analytic and numerical solutions. The construction is made possible by considering the development of a jump discontinuity in the solution of scalar quasilinear equations with piecewise smooth data. This is a simple generalization of a discussion by Lax [2].

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ER -

A test problem for numerical schemes for nonlinear hyperbolic equations

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