Convergence analysis and numerical solution of the Benjamin-Bona-Mahony equation by Lie-Trotter splitting

Fatma Zürnaci; Nurcan Gücüyenen Kaymak; Muaz Seydaoğlu; Gamze Tanoğlu

doi:10.3906/mat-1603-94

Convergence analysis and numerical solution of the Benjamin-Bona-Mahony equation by Lie-Trotter splitting

Fatma Zürnaci^*, Nurcan Gücüyenen Kaymak, Muaz Seydaoğlu, Gamze Tanoğlu

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.

Original language	English
Pages (from-to)	1471-1483
Number of pages	13
Journal	Turkish Journal of Mathematics
Volume	42
Issue number	3
DOIs	https://doi.org/10.3906/mat-1603-94
Publication status	Published - 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© TÜBI˙KTAK.

Keywords

Benjamin-Bona-Mahony equation
Convergence analysis
Lie-Trotter splitting

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10.3906/mat-1603-94

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title = "Convergence analysis and numerical solution of the Benjamin-Bona-Mahony equation by Lie-Trotter splitting",

abstract = "In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.",

keywords = "Benjamin-Bona-Mahony equation, Convergence analysis, Lie-Trotter splitting",

author = "Fatma Z{\"u}rnaci and {G{\"u}c{\"u}yenen Kaymak}, Nurcan and Muaz Seydaoğlu and Gamze Tanoğlu",

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language = "English",

volume = "42",

pages = "1471--1483",

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T1 - Convergence analysis and numerical solution of the Benjamin-Bona-Mahony equation by Lie-Trotter splitting

AU - Zürnaci, Fatma

AU - Gücüyenen Kaymak, Nurcan

AU - Seydaoğlu, Muaz

AU - Tanoğlu, Gamze

N1 - Publisher Copyright: © TÜBI˙KTAK.

PY - 2018

Y1 - 2018

N2 - In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.

AB - In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.

KW - Benjamin-Bona-Mahony equation

KW - Convergence analysis

KW - Lie-Trotter splitting

UR - http://www.scopus.com/inward/record.url?scp=85046716649&partnerID=8YFLogxK

U2 - 10.3906/mat-1603-94

DO - 10.3906/mat-1603-94

M3 - Article

AN - SCOPUS:85046716649

SN - 1300-0098

VL - 42

SP - 1471

EP - 1483

JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

IS - 3

ER -

Convergence analysis and numerical solution of the Benjamin-Bona-Mahony equation by Lie-Trotter splitting

Abstract

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Keywords

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