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


Zurnaci F. , Gucuyenen Kaymak N., Seydaoglu M., Tanoglu G.

TURKISH JOURNAL OF MATHEMATICS, cilt.42, ss.1471-1483, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 42 Konu: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1603-94
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.1471-1483

Özet

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.