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

Authors

FATMA ZÜRNACI
NURCAN GÜCÜYENEN KAYMAK
MUAZ SEYDAOĞLU
GAMZE TANOĞLU

DOI

10.3906/mat-1603-94

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

Lie-Trotter splitting, convergence analysis, Benjamin-Bona-Mahony equation

First Page

1471

Last Page

1483

Recommended Citation

ZÜRNACI, FATMA; KAYMAK, NURCAN GÜCÜYENEN; SEYDAOĞLU, MUAZ; and TANOĞLU, GAMZE (2018) "Convergence analysis and numerical solution of the Benjamin-Bona-Mahony equation by Lie-Trotter splitting," Turkish Journal of Mathematics: Vol. 42: No. 3, Article 57. https://doi.org/10.3906/mat-1603-94
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/57