Stable Explicit Schemes for Equations of the Schrödinger Type

DOI10.1137/0723019zbMath0618.65078OpenAlexW2010414883WikidataQ57397465 ScholiaQ57397465MaRDI QIDQ4728145

Tony F. Chan, Ding Lee, Long-jun Shen

Publication date: 1986

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0723019

zbMATH Keywords

conditional stabilitydissipative termexplicit finite difference schemesLax-Wendroff techniqueleast restrictive stabilityparabolic equations of Schrödinger type

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Heat equation (35K05) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Applications to the sciences (65Z05)

Related Items (14)

Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations ⋮ Novel explicit finite-difference schemes for time-dependent Schrödinger equations ⋮ Domain decomposition method for nonlinear generalized Schrödinger-type systems: Semi-discrete problem ⋮ PARABOLIC EQUATION DEVELOPMENT IN THE TWENTIETH CENTURY ⋮ Explicit dissipative schemes for boundary problems of generalized Schrödinger systems ⋮ HIGH-ORDER ACCURATE NUMERICAL SCHEMES FOR THE PARABOLIC EQUATION ⋮ An accurate approximation of exponential integrators for the Schrödinger equation ⋮ A nonlinear nonstandard finite difference scheme for the linear time-dependent Schrödinger equation ⋮ Mathematical and computational methods for semiclassical Schrödinger equations ⋮ Difference schemes for the parabolic wave equation in ocean acoustics ⋮ On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime ⋮ A well-balanced and asymptotic-preserving scheme for the one-dimensional linear Dirac equation ⋮ Multiple array processors for ocean acoustic problems ⋮ A blow-up problem for a nonlinear heat equation in the complex plane of time

This page was built for publication: Stable Explicit Schemes for Equations of the Schrödinger Type