Convergence of Finite Difference Schemes: Matrix Versus Kernel Analysis

M. Ben-Artzi; J. P. Croisille; D. Fishelov

doi:10.1007/978-3-031-20432-6_8

Convergence of Finite Difference Schemes: Matrix Versus Kernel Analysis

M. Ben-Artzi, J. P. Croisille^*, D. Fishelov

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We consider the convergence analysis of a compact finite difference scheme for the equation ut+∂4∂x4u=0. The discrete in space, continuous in time approximation is (formula presented) is the discrete biharmonic operator (DBO) operator. The error (formula presented) for sufficiently smooth data. This problem serves as a model to compare an analytic approach, based on functional analysis and a purely matrix approach. The matrix approach benefits from tools of matrix theory of linear algebra and from known results for the solution of a set of ordinary differential equations. The functional analytic approach utilizes the connection to the continuous problem.

Original language	English
Title of host publication	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021
Editors	Jens M. Melenk, Joachim Schöberl, Ilaria Perugia, Christoph Schwab
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	155-168
Number of pages	14
ISBN (Print)	9783031204319
DOIs	https://doi.org/10.1007/978-3-031-20432-6_8
State	Published - 2023
Event	13th International Conference on Spectral and High Order Methods, ICOSAHOM 2021 - Vienna, Austria Duration: 12 Jul 2021 → 16 Jul 2021

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	137
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	13th International Conference on Spectral and High Order Methods, ICOSAHOM 2021
Country/Territory	Austria
City	Vienna
Period	12/07/21 → 16/07/21

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Access to Document

10.1007/978-3-031-20432-6_8

Cite this

Ben-Artzi, M., Croisille, J. P., & Fishelov, D. (2023). Convergence of Finite Difference Schemes: Matrix Versus Kernel Analysis. In J. M. Melenk, J. Schöberl, I. Perugia, & C. Schwab (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021 (pp. 155-168). (Lecture Notes in Computational Science and Engineering; Vol. 137). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-20432-6_8

Ben-Artzi, M. ; Croisille, J. P. ; Fishelov, D. / Convergence of Finite Difference Schemes : Matrix Versus Kernel Analysis. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021. editor / Jens M. Melenk ; Joachim Schöberl ; Ilaria Perugia ; Christoph Schwab. Springer Science and Business Media Deutschland GmbH, 2023. pp. 155-168 (Lecture Notes in Computational Science and Engineering).

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Ben-Artzi, M, Croisille, JP & Fishelov, D 2023, Convergence of Finite Difference Schemes: Matrix Versus Kernel Analysis. in JM Melenk, J Schöberl, I Perugia & C Schwab (eds), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021. Lecture Notes in Computational Science and Engineering, vol. 137, Springer Science and Business Media Deutschland GmbH, pp. 155-168, 13th International Conference on Spectral and High Order Methods, ICOSAHOM 2021, Vienna, Austria, 12/07/21. https://doi.org/10.1007/978-3-031-20432-6_8

Convergence of Finite Difference Schemes: Matrix Versus Kernel Analysis. / Ben-Artzi, M.; Croisille, J. P.; Fishelov, D.
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021. ed. / Jens M. Melenk; Joachim Schöberl; Ilaria Perugia; Christoph Schwab. Springer Science and Business Media Deutschland GmbH, 2023. p. 155-168 (Lecture Notes in Computational Science and Engineering; Vol. 137).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Ben-Artzi M, Croisille JP, Fishelov D. Convergence of Finite Difference Schemes: Matrix Versus Kernel Analysis. In Melenk JM, Schöberl J, Perugia I, Schwab C, editors, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021. Springer Science and Business Media Deutschland GmbH. 2023. p. 155-168. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-031-20432-6_8

Convergence of Finite Difference Schemes: Matrix Versus Kernel Analysis

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