- Turkish Journal of Mathematics
- Vol: 42 Issue: 3
- Convergence analysis and numerical solution of the Benjamin-Bona-Mahony equation by Lie-Trotter spli...
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
Pages : 1471-1483
View : 8 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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