Publication

Analysis of smoothing operators in the solution of partial differential equations by explicit difference schemes

Houwen, P. J. V. D., Sommeijer, B. P. & Wubs, F. W., 1990, In : Applied numerical mathematics. 21 p.

Research output: Contribution to journalArticleAcademic

APA

Houwen, P. J. V. D., Sommeijer, B. P., & Wubs, F. W. (1990). Analysis of smoothing operators in the solution of partial differential equations by explicit difference schemes. Applied numerical mathematics.

Author

Houwen, P.J. van der ; Sommeijer, B.P. ; Wubs, F.W. / Analysis of smoothing operators in the solution of partial differential equations by explicit difference schemes. In: Applied numerical mathematics. 1990.

Harvard

Houwen, PJVD, Sommeijer, BP & Wubs, FW 1990, 'Analysis of smoothing operators in the solution of partial differential equations by explicit difference schemes', Applied numerical mathematics.

Standard

Analysis of smoothing operators in the solution of partial differential equations by explicit difference schemes. / Houwen, P.J. van der; Sommeijer, B.P.; Wubs, F.W.

In: Applied numerical mathematics, 1990.

Research output: Contribution to journalArticleAcademic

Vancouver

Houwen PJVD, Sommeijer BP, Wubs FW. Analysis of smoothing operators in the solution of partial differential equations by explicit difference schemes. Applied numerical mathematics. 1990.


BibTeX

@article{169e4fa3a6af47958f849c9469bfaffd,
title = "Analysis of smoothing operators in the solution of partial differential equations by explicit difference schemes",
abstract = "A smoothing technique for the “preconditioning” of the right-hand side of semidiscrete partial differential equations is analyzed. For a parabolic and a hyperbolic model problem, optimal smoothing matrices are constructed which result in a substantial amplification of the maximal stable integration step of arbitrary explicit time integrators when applied to the smoothed problem. This smoothing procedure is illustrated by integrating both linear and nonlinear parabolic and hyperbolic problems. The results show that the stability behaviour is comparable with that of the Crank-Nicolson method; furthermore, if the problem belongs to the problem class in which the time derivative of the solution is a smooth function of the space variables, then the accuracy is also comparable with that of the Crank-Nicolson method.",
keywords = "stability, smoothing, explicit integration methods, method of lines, initial boundary value problems in partial differential equa, numerical analysis",
author = "Houwen, {P.J. van der} and B.P. Sommeijer and F.W. Wubs",
note = "Relation: https://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)",
year = "1990",
language = "English",
journal = "Applied numerical mathematics",
issn = "0168-9274",
publisher = "ELSEVIER SCIENCE BV",

}

RIS

TY - JOUR

T1 - Analysis of smoothing operators in the solution of partial differential equations by explicit difference schemes

AU - Houwen, P.J. van der

AU - Sommeijer, B.P.

AU - Wubs, F.W.

N1 - Relation: https://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)

PY - 1990

Y1 - 1990

N2 - A smoothing technique for the “preconditioning” of the right-hand side of semidiscrete partial differential equations is analyzed. For a parabolic and a hyperbolic model problem, optimal smoothing matrices are constructed which result in a substantial amplification of the maximal stable integration step of arbitrary explicit time integrators when applied to the smoothed problem. This smoothing procedure is illustrated by integrating both linear and nonlinear parabolic and hyperbolic problems. The results show that the stability behaviour is comparable with that of the Crank-Nicolson method; furthermore, if the problem belongs to the problem class in which the time derivative of the solution is a smooth function of the space variables, then the accuracy is also comparable with that of the Crank-Nicolson method.

AB - A smoothing technique for the “preconditioning” of the right-hand side of semidiscrete partial differential equations is analyzed. For a parabolic and a hyperbolic model problem, optimal smoothing matrices are constructed which result in a substantial amplification of the maximal stable integration step of arbitrary explicit time integrators when applied to the smoothed problem. This smoothing procedure is illustrated by integrating both linear and nonlinear parabolic and hyperbolic problems. The results show that the stability behaviour is comparable with that of the Crank-Nicolson method; furthermore, if the problem belongs to the problem class in which the time derivative of the solution is a smooth function of the space variables, then the accuracy is also comparable with that of the Crank-Nicolson method.

KW - stability

KW - smoothing

KW - explicit integration methods

KW - method of lines

KW - initial boundary value problems in partial differential equa

KW - numerical analysis

M3 - Article

JO - Applied numerical mathematics

JF - Applied numerical mathematics

SN - 0168-9274

ER -

ID: 14408539