TY  - JOUR
TI  - Convergence analysis and numerical solution of the Benjamin–Bona–Mahony equation by Lie–Trotter splitting
AB  - In this paper, an operator splitting method is used to analyze nonlinear Benjamin–Bona–Mahony-typeequations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie–Trottersplitting is applied to the equation. The local error bounds are obtained by using the approach based on the differentialtheory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global errorestimate is obtained via Lady Windermere’s fan argument. Finally, to confirm the expected convergence order, numericalexamples are studied.
AU  - ZÜRNACI, Fatma
AU  - TANOĞLU, Gamze
AU  - SEYDAOGLU, MUAZ
AU  - GÜCÜYENEN KAYMAK, Nurcan
DO  - 10.3906/mat-1603-94
PY  - 2018
JO  - Turkish Journal of Mathematics
VL  - 42
IS  - 3
SN  - 1300-0098
SP  - 1471
EP  - 1483
DB  - TRDizin
UR  - http://search/yayin/detay/348748
ER  -