title: Compact fourth-order finite difference method for solving differential equations.
abstract: We present a fourth-order finite difference (FD) method for solving two-dimensional partial differential equations. The FD operator uses a compact nine-point stencil on a regular square grid. Despite the regular grid, Dirichlet boundary conditions can be applied on an arbitrarily shaped boundary without resorting to the usual stepped approximation. We demonstrate the superior convergence of the method over second-order techniques by solving the Schrödinger equation for an electron in a semiconductor quantum dot with a smoothly varying potential which generates classically chaotic dynamics.
authors.affiliation: School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom.
authors.forename: P B
authors.initials: PB
authors.lastname: Wilkinson
authors.forename: T M
authors.initials: TM
authors.lastname: Fromhold
authors.forename: C R
authors.initials: CR
authors.lastname: Tench
authors.forename: R P
authors.initials: RP
authors.lastname: Taylor
authors.forename: A P
authors.initials: AP
authors.lastname: Micolich