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International Journal of Differential Equations
Volume 2016 (2016), Article ID 6930758, 12 pages
http://dx.doi.org/10.1155/2016/6930758
Research Article

Error Analysis of an Implicit Spectral Scheme Applied to the Schrödinger-Benjamin-Ono System

Departamento de Matemáticas, Universidad del Valle, Calle 13 Nro. 100-00, Cali, Colombia

Received 30 July 2016; Accepted 10 October 2016

Academic Editor: Wen-Xiu Ma

Copyright © 2016 Juan Carlos Muñoz Grajales. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We develop error estimates of the semidiscrete and fully discrete formulations of a Fourier-Galerkin numerical scheme to approximate solutions of a coupled nonlinear Schrödinger-Benjamin-Ono system that describes the motion of two fluids with different densities under capillary-gravity waves in a deep water regime. The accuracy of the numerical solver is checked using some exact travelling wave solutions of the system.