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 ...

The nonlinear two-dimensional forced-convection boundary-layer magneto hydrodynamic MHD incompressible flow of nanofluid over a horizontal stretching flat plate with variable magnetic field including the viscous dissipation effect is solved using the homotopy perturbation method HPM . In the present work, our results of the HPM are compared with the results of simulation using the finite differ...

Reciprocity is applied to the situation where numerical simulations are needed for a number of source locations but relatively a few receiver positions. By invoking source-receiver reciprocity, the number of simulations can be generally reduced to three times the number of receiver positions. The procedure is illustrated for a heterogeneous medium with both single-force and double-couple source...

As shown in previous papers, mathematical simulation can be useful in the design of drug delivery systems. We present a finite-difference approximation to the drug mass transfer rate from dissolving cylindrical drug-containing compacts, consisting of alternating layers of drug and inert material. Results are compared with a recent analytical solution to the same problem and with experiment. The...

Generalized Fibonacci-like sequences appear in finite difference approximations of the Partial Differential Equations based upon replacing partial differential equations by finite difference equations. This paper studies properties of the generalized Fibonacci-like sequence . It is shown that this sequence is periodic with the period ( ) if | | .

Radial basis functions (RBFs) are receiving much attention as a tool for solving PDEs because of their ability to achieve spectral accuracy also with unstructured node layouts. Such node sets provide both geometric flexibility and opportunities for local node refinement. In spite of requiring a somewhat larger total number of nodes for the same accuracy, RBF-generated finite difference (RBF-FD)...