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Finite difference methods for the heat equation with a nonlocal boundary condition

Vidar Thomée (Institutionen för matematiska vetenskaper, matematik) ; A. S. Vasudeva Murthy
Journal of Computational Mathematics (0254-9409). Vol. 33 (2015), p. 17-32.
[Artikel, refereegranskad vetenskaplig]

We consider the numerical solution by finite difference methods of the heat equation in one space dimension, with a nonlocal integral boundary condition, resulting from the truncation to a finite interval of the problem on a semi-infinite interval. We first analyze the forward Euler method, and then the theta-method for 0 < theta <= 1, in both cases in maximum-norm, showing O(h(2) + k) error bounds, where h is the mesh-width and k the time step. We then give an alternative analysis for the case theta = 1/2, the Crank-Nicolson method, using energy arguments, yielding a O(h(2) + k(3/2)) error bound. Special attention is given the approximation of the boundary integral operator. Our results are illustrated by numerical examples.

Nyckelord: Heat equation, Artificial boundary conditions, unbounded domains, product quadrature

Denna post skapades 2015-01-09. Senast ändrad 2015-01-16.
CPL Pubid: 210365


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)


Numerisk analys

Chalmers infrastruktur