Accurate numerical resolution of transients in initial-boundary value problems for the heat equation

AMS Citation:
Flyer, N., and B. Fornberg, 2003: Accurate numerical resolution of transients in initial-boundary value problems for the heat equation. Journal of Computational Physics, 184, 526-539, doi:10.1016/S0021-9991(02)00034-7.
Date:2003-01-20
Resource Type:article
Title:Accurate numerical resolution of transients in initial-boundary value problems for the heat equation
Abstract: If the initial and boundary data for a PDE do not obey an infinite set of compatibility conditions, singularities will arise in the solution at the corners of the initial time–space domain. For dissipative equations, such as the 1-D heat equation or 1-D convection–diffusion equations, the impacts of these singularities are short lived. However, they can cause a very severe loss of numerical accuracy if we are interested in transient solutions. The phenomenon has been described earlier from a theoretical standpoint. Here, we illustrate it graphically and present a simple remedy which, with only little extra cost and effort, restores full numerical accuracy.
Peer Review:Refereed
Copyright Information:Copyright 2003 Elsevier.
OpenSky citable URL: ark:/85065/d7vx0j4m
Publisher's Version: 10.1016/S0021-9991(02)00034-7
Author(s):
  • Natasha Flyer - NCAR/UCAR
  • Bengt Fornberg
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