A linearly implicit finite-difference scheme for the one-dimensional porous medium equation

Hoff, David

doi:10.1090/S0025-5718-1985-0790642-6

A linearly implicit finite-difference scheme for the one-dimensional porous medium equation

Author: David Hoff
Journal: Math. Comp. 45 (1985), 23-33
MSC: Primary 65M15; Secondary 76S05
DOI: https://doi.org/10.1090/S0025-5718-1985-0790642-6
MathSciNet review: 790642
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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 $\Delta t/\Delta x \leqslant {\text{constant}}$ .

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