JSTOR Daily

A SECOND ORDER BDF NUMERICAL SCHEME WITH VARIABLE STEPS FOR THE CAHN-HILLIARD EQUATION

We present and analyze a second order in time variable step BDF2 numerical scheme for the Cahn-Hilliard equation. The construction relies on a second order backward difference, convex-splitting ...
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 ...
UMass Lowell

Catalog : MECH.5200 Numerical Methods for Partial Differential Equations (Formerly 22.520)

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...
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 ...
Nature

Maxwell's Equations and Numerical Methods in Electromagnetic Wave Propagation

Maxwell's equations form the cornerstone of electromagnetic theory, offering a complete description of how electric and magnetic fields interact with matter. In combination with state‐of‐the‐art ...
Risk

Alternating direction implicit finite difference schemes for the Heston-Hull-White partial differential equation

In this paper we investigate the effectiveness of alternating direction implicit (ADI) time-discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial ...