Nature

Difference Equations and Their Applications

Difference equations, serving as the discrete analogue to differential equations, have long been a linchpin in the study of dynamic systems. These equations define sequences recursively, and their ...
JSTOR Daily

ON THE DERIVATION OF HIGHEST-ORDER COMPACT FINITE DIFFERENCE SCHEMES FOR THE ONE- AND TWO-DIMENSIONAL POISSON EQUATION WITH DIRICHLET BOUNDARY CONDITIONS

SIAM Journal on Numerical Analysis, Vol. 51, No. 4 (2013), pp. 2470-2490 (21 pages) The primary aim of this paper is to answer the question, What are the highest-order five-or nine-point compact ...
Simon Fraser University

Example 14.10: Systems of Differential Equations

For this system, the initial values for the concentrations are derived from equilibrium considerations (as a function of parameters) or are provided as known values. The experiment used to collect the ...
JSTOR Daily

A Survey of Some Applications of Probability and Stochastic Control Theory to Finite Difference Methods for Degenerate Elliptic and Parabolic Equations

Finite difference methods for degenerate linear and (certain) nonlinear elliptic and parabolic equations are analyzed from a probabilistic point of view, and probabilistic methods are used to show ...
Risk

Numerical simulation and applications of the convection–diffusion–reaction equation with the radial basis function in a finite-difference mode

This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...