In this paper, we present a numerical approach to a class of nonlinear reactiondiffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. ...

Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems.

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.