The numerical simulation of shallow water acoustic propagation has given rise to a wide variety of modeling techniques with various degrees of accuracy. One technique, involving finite difference methods, is more commonly used in the description of seismic propagation but also occurs in the shallow water propagation literature. This word reported here involves the application of finite differen...

The convergence of a class of combined spectral-finite difference methods using Hermite basis, applied to the Fokker-Planck equation, is studied. It is shown that the Hermite based spectral methods are convergent with spectral accuracy in weighted Sobolev space. Numerical results indicating the spectral convergence rate are presented. A velocity scaling factor is used in the Hermite basis and i...

We provide error analyses for explicit, implicit, and semi-implicit monotone finitedifference schemes on uniform meshes with nonlocal numerical fluxes. We are motivated by finite-difference discretizations of certain long-wave (Sobolev) regularizations of the conservation laws that explicitly add a dispersive term as well as a nonlinear dissipative term. We also develop certain relationships be...

In this paper a singularly perturbed reaction-diffusion partial differential equation in two space dimensions is examined. By means of an appropriate decomposition, we describe the asymptotic behaviour of the solution of problems of this kind. A central finite difference scheme is constructed for this problem which involves an appropriate Shishkin mesh. We prove that the numerical approximation...

The vibration of an elastic beam experiencing vortex-induced vibration is numerically analyzed through a wake-oscillator model using the finite differences method. The influence of the excited mode, the initial velocity, the shedding pulsation and the mass ratio on the energy transfer among modes and the vibration amplitude is determined. Multiple frequencies are detected, and the power spectra...

8 In this paper, we study the error of a second order finite difference scheme for the one-dimensional 9 convection-diffusion equation. We consider non-smooth initial conditions commonly encountered in 10 financial pricing applications. For these initial conditions, we establish the explicit expression of the 11 quantization error, which is loosely defined as the error of the numerical solution...

Meshfree finite difference methods for the Poisson equation approximate the Laplace operator on a point cloud. Desirable are positive stencils, i.e. all neighbor entries are of the same sign. Classical least squares approaches yield large stencils that are in general not positive. We present an approach that yields stencils of minimal size, which are positive. We provide conditions on the point...

TlWi paper is concerned with tILe numerical solution of the American option \la/nalion problem formulated as a parabolic free boundary/inilial value model. For this we introduce and analyze scveral front-tracking finite difference methods and compare I.hcm with the commonly used binomial and linear complementarity techniques. The numerical experiments performed indicate that the front-tracking ...

The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exi...