Numerical solution of a parabolic transmission problem

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.

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Original source : http://imajna.oxfordjournals.org/cgi/content/short...