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...

An implicit finite difference scheme is derived which achieves exact results for the area, centroid, variance, skewness and kurtosis (flatness) of solutions to the unforced advection-diffusion equation ∂ t c + λ c + u ∂ x c − κ ∂ 2 x c = 0. Sufficient conditions for computational stability are that the grid spacing ∆x and time step ∆t be small enough that |u| ∆x κ < 12 1/2 , |u| ∆t ∆x < 1 2 1/2...

Systems of m PDEs of Adv-Diff-React type have the following form, where the dependent variables (unknowns) are u = (u j (x, t)) m j=1 : Systems of m PDEs of Adv-Diff-React type have the following form, where the dependent variables (unknowns) are u = (u j (x, t)) m j=1 : ∂ ∂t u j + ∇ · (a j u j) = ∇ · (D j ∇u j) + f j , These PDEs model a lot of important phenomena, see These PDEs model a lot o...

Coupling between adjacent Finite Ground Coplanar (FGC) waveguides as a function of the line geometry is presented for the first time. A two Dimension-Finite Difference Time Domain (2D-FDTD) analysis and measurements are used to show that the coupling decreases as the line to line separation and the ground plane width increases. Furthermore, it is shown that for a given spacing between the cente...

We continue our study on the approximation of a system of partial differential equations recently proposed by Hadeler and Kuttler to model the dynamics of growing sandpiles on a flat bounded table. The novelty here is the introduction of (infinite) walls on the boundary of the domain and the corresponding modification of boundary conditions for the standing and for the rolling layers. An explic...

This is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A ...