LAX-WENDROFF METHODS FOR HYPOERBOLIC HISTORY VALUE PROBLEMS.

Peter Markowich; Michael Renardy

doi:10.1137/0721002

LAX-WENDROFF METHODS FOR HYPOERBOLIC HISTORY VALUE PROBLEMS.

Peter Markowich^*, Michael Renardy

^*Corresponding author for this work

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

13 Scopus citations

Abstract

Hyperbolic history value problems have the feature that globally (in time) smooth solutions exist if the data are sufficiently small and that solutions develop singularities for large data. The authors prove (second order) convergence of the Lax-Wendroff method for smooth solutions and investigate numerically the dependence of the initial data. They demonstrate the occurrence of shock type singularities and compare the results to the quasilinear wave equation (without Volterra term).

Original language	English (US)
Pages (from-to)	24-51
Number of pages	28
Journal	SIAM Journal on Numerical Analysis
Volume	21
Issue number	1
DOIs	https://doi.org/10.1137/0721002
State	Published - 1984
Externally published	Yes

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics
Numerical Analysis

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10.1137/0721002

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@article{a4eae71b45914aa98fe46af3e3946768,

title = "LAX-WENDROFF METHODS FOR HYPOERBOLIC HISTORY VALUE PROBLEMS.",

abstract = "Hyperbolic history value problems have the feature that globally (in time) smooth solutions exist if the data are sufficiently small and that solutions develop singularities for large data. The authors prove (second order) convergence of the Lax-Wendroff method for smooth solutions and investigate numerically the dependence of the initial data. They demonstrate the occurrence of shock type singularities and compare the results to the quasilinear wave equation (without Volterra term).",

author = "Peter Markowich and Michael Renardy",

year = "1984",

doi = "10.1137/0721002",

language = "English (US)",

volume = "21",

pages = "24--51",

journal = "SIAM Journal on Numerical Analysis",

issn = "0036-1429",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "1",

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TY - JOUR

T1 - LAX-WENDROFF METHODS FOR HYPOERBOLIC HISTORY VALUE PROBLEMS.

AU - Markowich, Peter

AU - Renardy, Michael

PY - 1984

Y1 - 1984

N2 - Hyperbolic history value problems have the feature that globally (in time) smooth solutions exist if the data are sufficiently small and that solutions develop singularities for large data. The authors prove (second order) convergence of the Lax-Wendroff method for smooth solutions and investigate numerically the dependence of the initial data. They demonstrate the occurrence of shock type singularities and compare the results to the quasilinear wave equation (without Volterra term).

AB - Hyperbolic history value problems have the feature that globally (in time) smooth solutions exist if the data are sufficiently small and that solutions develop singularities for large data. The authors prove (second order) convergence of the Lax-Wendroff method for smooth solutions and investigate numerically the dependence of the initial data. They demonstrate the occurrence of shock type singularities and compare the results to the quasilinear wave equation (without Volterra term).

UR - http://www.scopus.com/inward/record.url?scp=0021377643&partnerID=8YFLogxK

U2 - 10.1137/0721002

DO - 10.1137/0721002

M3 - Article

AN - SCOPUS:0021377643

SN - 0036-1429

VL - 21

SP - 24

EP - 51

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 1

ER -

LAX-WENDROFF METHODS FOR HYPOERBOLIC HISTORY VALUE PROBLEMS.

Abstract

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