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, vol.42, no.3, pp.1471-1483, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1603-94
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1471-1483
  • Keywords: Lie-Trotter splitting, convergence analysis, Benjamin-Bona-Mahony equation, WAVE SOLUTIONS, MODEL
  • Istanbul Technical University Affiliated: No

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.