We suggest a finite dfference scheme for the Camassa-Holm equation that can handle general H1 initial data. The form of the difference scheme is judiciously chosen to ensure that it satisfies a total energy inequality. We prove that the difference scheme converges strongly in H1 towards an exact dissipative weak solution of Camassa-Holm equation.

In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18] to compute the Saint-Venant system of shallow water equations with pollutant propagation, which is described by a transport equation. The motivation is that the high order anti-diffusive WENO scheme for conservation laws produces sharp resoluti...

We suggest a finite dfference scheme for the Camassa-Holm equation that can handle general H1 initial data. The form of the difference scheme is judiciously chosen to ensure that it satisfies a total energy inequality. We prove that the difference scheme converges strongly in H1 towards an exact dissipative weak solution of Camassa-Holm equation.

High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in [32, 7, 6]. Recently, it has been observed in [3] that this approach may have some computational issues and shortcomings. In this paper, a modification to the high order path-conservative scheme in [7], based on the high order finite volume WENO scheme with subcell resolution and utilizing...

In this paper a time-dependent moving-grid method is described to numerically solve time-dependent partial differential equations (PDEs) in one space dimensions involving fine scale structures such as steep moving fronts, emerging steep layers, pulses and shocks. Smoothing in the spatial direction is employed to control grid clustering and expansion. Additional smoothing in the temporal directi...

This paper is devoted to the numerical comparison of methods applied to solve problems with nonlocal boundary conditions. Four numerical methods are compared, namely, finite differences method, Galerkin method, Keller Box scheme and orthogonal spline collocation method. Mathematics Subject Classification: 74S05, 74S20, 74S30, 74H15

We develop and test a finite difference scheme for the Vlasov-Manev Equation in one space and one velocity dimension. The Manev correction to the Newtonian potential produces visible qualitative differences in the behaviour of stellar systems; the most notable effect observed in this paper is a stabilisation of the separate identities of two Maxwellian concentrations at different locations. 199...