TY - JOUR
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 -