Introduction and study of fourth order theta schemes for linear wave equations

Juliette Chabassier; Sébastien Imperiale

doi:10.1016/j.cam.2012.12.023

Introduction and study of fourth order theta schemes for linear wave equations

Juliette Chabassier, Sébastien Imperiale

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

Abstract

A new class of high order, implicit, three time step schemes for semi-discretized wave equations is introduced and studied. These schemes are constructed using the modified equation approach, generalizing the θ-scheme. Their stability properties are investigated via an energy analysis, which enables us to design super-convergent schemes and also optimal stable schemes in terms of consistency errors. Specific numerical algorithms for the fully discrete problem are tested and discussed, showing the efficiency of our approach compared to second order θ-schemes.

Original language	English
Pages (from-to)	194-212
Number of pages	19
Journal	Journal of Computational and Applied Mathematics
Volume	245
DOIs	https://doi.org/10.1016/j.cam.2012.12.023
Publication status	Published - 1 Jun 2013
Externally published	Yes

Keywords

High order numerical methods
Modified equation
Theta-scheme
Time discretization
Wave equations

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10.1016/j.cam.2012.12.023

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title = "Introduction and study of fourth order theta schemes for linear wave equations",

abstract = "A new class of high order, implicit, three time step schemes for semi-discretized wave equations is introduced and studied. These schemes are constructed using the modified equation approach, generalizing the θ-scheme. Their stability properties are investigated via an energy analysis, which enables us to design super-convergent schemes and also optimal stable schemes in terms of consistency errors. Specific numerical algorithms for the fully discrete problem are tested and discussed, showing the efficiency of our approach compared to second order θ-schemes.",

keywords = "High order numerical methods, Modified equation, Theta-scheme, Time discretization, Wave equations",

author = "Juliette Chabassier and S{\'e}bastien Imperiale",

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T1 - Introduction and study of fourth order theta schemes for linear wave equations

AU - Chabassier, Juliette

AU - Imperiale, Sébastien

PY - 2013/6/1

Y1 - 2013/6/1

N2 - A new class of high order, implicit, three time step schemes for semi-discretized wave equations is introduced and studied. These schemes are constructed using the modified equation approach, generalizing the θ-scheme. Their stability properties are investigated via an energy analysis, which enables us to design super-convergent schemes and also optimal stable schemes in terms of consistency errors. Specific numerical algorithms for the fully discrete problem are tested and discussed, showing the efficiency of our approach compared to second order θ-schemes.

AB - A new class of high order, implicit, three time step schemes for semi-discretized wave equations is introduced and studied. These schemes are constructed using the modified equation approach, generalizing the θ-scheme. Their stability properties are investigated via an energy analysis, which enables us to design super-convergent schemes and also optimal stable schemes in terms of consistency errors. Specific numerical algorithms for the fully discrete problem are tested and discussed, showing the efficiency of our approach compared to second order θ-schemes.

KW - High order numerical methods

KW - Modified equation

KW - Theta-scheme

KW - Time discretization

KW - Wave equations

U2 - 10.1016/j.cam.2012.12.023

DO - 10.1016/j.cam.2012.12.023

M3 - Article

AN - SCOPUS:84872450744

SN - 0377-0427

VL - 245

SP - 194

EP - 212

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

Introduction and study of fourth order theta schemes for linear wave equations

Abstract

Keywords

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