Abstract
We present and analyze a linearly implicit finite-difference scheme for computing approximate solutions and interface curves for the porous medium equation in one space variable. Our scheme requires only that linear, tridiagonal systems of equations be solved at each time step. We derive error bounds for the approximate interface curves as well as for the approximate solutions under the rather mild mesh condition Δ t / Δ x ⩽ constant \Delta t/\Delta x \leqslant {\text {constant}} .
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