A numerical method for the Benjamin-Ono equation

Existence and uniqueness for a nonlocal internal wave model

“…Some numerical schemes to approximate solutions of scalar unidirectional Benjamin-Ono type equations were proposed for instance by Pelloni and Dougalis [19,18], James and Weideman [11], Miloh et al [16] and Tomée and Vasudeva [21]. Also, Choi and Camassa [8] solved a system similar to Eq.…”

Error Estimate of the Fourier Collocation Method for the Benjamin-Ono Equation

“…The special case F{U) -U^ is the BO equation. Fourier methods for the BO equation have been studied by many authors [4,[9][10][11][12]. In recent work [11], it is proved that error of the Fourier Galerkin (FC) method for the BO equation is of the order <^(iV^~'') in L^-norm for the analytic solution in H^ An optimal error bound Û(N^^^~'') of the method in H^^^-norm is obtained in [4].…”

Convergence of finite difference schemes for the Benjamin–Ono equation

“…While there are several numerical methods for the BO equation which perform well in practice, indeed better than the one presented here, see [3] for a recent comparison of different numerical methods, we emphasize that we here prove the convergence of our proposed scheme. Having said this, there are results concerning error estimates for the BO equation in [19,14,5]. However, error estimate analysis a priori assumes existence of solutions of the underlying equation, while our convergence analysis, as a by-product, can be viewed as a constructive proof for the existence of solutions of the BO equation (1.1).…”

“…However, error estimate analysis a priori assumes existence of solutions of the underlying equation, while our convergence analysis, as a by-product, can be viewed as a constructive proof for the existence of solutions of the BO equation (1.1). It is worth mentioning that the scheme under consideration in this paper is similar to the scheme analyzed in [19], the only difference being that a different discretization of Hilbert transform is introduced in this paper.…”