Finite difference methods for the heat equation with a nonlocal boundary condition
Artikel i vetenskaplig tidskrift, 2015

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.

Artificial boundary conditions

product quadrature

Heat equation

unbounded domains

Författare

Vidar Thomee

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

A. S. Vasudeva Murthy

Tata Institute of Fundamental Research

Journal of Computational Mathematics

0254-9409 (ISSN)

Vol. 33 17-32

Ämneskategorier

Beräkningsmatematik

Fundament

Grundläggande vetenskaper

DOI

10.4208/jcm.1406-m4443