The goal of this work is to determine classes of traveling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz.

We develop a new efficient second-order finite difference scheme for two-dimensional problem of contaminant in groundwater flow. Theoretical analysis shows that the scheme is second-order convergence in the L2 norm and is unconditionally stable. Numerical results demonstrate that the error measures of the second-order scheme are several times smaller than those of the standard implicit finite d...

This paper describes a technique for timestamping data from an array of sensors. This is a challenging issue that needs to be solved for the magnetometry-based navigation system presented here. This system uses finite difference schemes to evaluate spatial and time derivatives of a vector field. The accuracy of the timestamping method is critical. In the context of this particular application, ...

We prove that a certain finite difference scheme converges to the weak solution of the Cauchy problem on a finite interval with periodic boundary conditions for the Camassa– Holm equation ut−uxxt +3uux−2uxuxx−uuxxx = 0 with initial data u|t=0 = u0 ∈ H1([0, 1]). Here it is assumed that u0 − u′′ 0 ≥ 0 and in this case, the solution is unique, globally defined, and energy preserving.

In this paper, we provide stability and convergence analysis for a class of finite difference schemes for unsteady incompressibleNavier-Stokes equations in vorticity-stream function formulation. The no-slip boundary condition for the velocity is converted into local vorticity boundary conditions. Thom’s formula, Wilkes’ formula, or other local formulas in the earlier literature can be used in t...

Difference equations of the form X ( t ) = F * ( t ) X ( t 1 ) F ( t ) F * ( t ) X ( t 1)G(t)[ l + G * ( t ) X ( t 1)G(t)]t G * ( t ) X ( t 1)F(t)+ Q(t ) and their associated Hermitian matrices H ( t ) = (0 v F* _C,C.)(t) are studied. Solution of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to t...

Modal analysis of the flux reconstruction (FR) formulation is performed to obtain the semi-discrete and fully-discrete dispersion relations, using which, the wave properties of physical as well as spurious modes are characterized. The effect of polynomial order, correction function and solution points on the dispersion, dissipation and relative energies of the modes are investigated. Using this...

We consider the stability of a finite difference scheme with two weight parameters for a hyperbolic equation with nonlocal integral boundary conditions. We obtain stability region in the complex plane by investigating the characteristic equation of a difference scheme using the root criterion.

A conservative three-level linear finite difference scheme for the numerical solution of the initial-boundary value problem of Rosenau-KdV equation is proposed.The difference scheme simulates two conservative quantities of the problemwell.The existence and uniqueness of the difference solution are proved. It is shown that the finite difference scheme is of second-order convergence and unconditi...

In this work, we propose a model of nonlocal partial differential equation (PDE) with deviated type function in the boundary condition. This model is solved numerically by finite difference method (FDM) using variable space grid (VSG) technique. The results obtained by this method are in a good agreement with the solution of the corresponding rectangular domain problem. Also, we investigated th...