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IMA Journal of Numerical Analysis Advance Access published online on September 10, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drn077
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Numerical solution of a parabolic transmission problem

Bosko S. Jovanovic{dagger}

Faculty of Mathematics, University of Belgrade, 11000 Belgrade, Serbia

Lubin G. Vulkov

Department of Mathematics, University of Rousse, 7017 Rousse, Bulgaria

{dagger} Corresponding author. Email: bosko{at}matf.bg.ac.yu

Received on 7 January 2008. Revised on 2 September 2008.


  Abstract

In this paper we investigate an initial boundary-value problem for a one-dimensional parabolic equation in two disconnected intervals. A finite-difference scheme approximating this problem is proposed and analysed. An estimate of the convergence rate, compatible with the smoothness of the input data (up to a logarithmic factor of the mesh size), is obtained.

Key Words: transmission problem; initial boundary-value problem; disconnected domains; Sobolev spaces; finite differences; convergence rate


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