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/lbN du/dx pu = 4>o(t) , x = a, f > Q du/dx + qu = (piit) , x = b, where p, q are constants, <bo(t) and <bi(t) are bounded as t —> », and there are no discontinuities in the initial or boundary conditions, or at the corners of R. In addition, we assume g(x) > 0, for a < x < b. Several authors (e.g. [l]-[5]) have considered the equation (1) subject to (la) and (lb) for the particular case when p ^ 0 and q S: 0. These conditions are not imposed in this paper. In [6] Keast and Mitchell have considered the problem of the present paper with g(x) = 1.

The stability of difference approximations to a selfadjoint parabolic equation, under derivative boundary conditions