A NUMERICAL PROCEDURE FOR DIFFUSION SUBJECT TO THE SPECIFICATION OF MASS

An application of the maximum principle yields an a priori estimate for the derivative u(x) of the solution u of u(t) = u(xx) + s, 0 < x < 1, 0 < t less-than-or-equal-to T, subject to u(x, 0) = f(x), 0 < x < 1, u(1, t) = g(t), 0 < t less-than-or-equal-to T, and the specification of mass integral-b(t)/0 u(x, t) dx = m(t), 0 < b(t) < 1. From this a priori estimate the continuous dependence of the solution u on the data is established. The maximum principle can also be applied to a numerical scheme for the derivative of u. Thus convergence is shown for an elementary numerical scheme. The article concludes with the results of some numerical experiments.