## Explicit variable time-step method for implicit moving boundary problems.(English)Zbl 0801.65122

A one-dimensional diffusion equation $$\partial u/ \partial t = \partial^ 2 u/ \partial x^ 2 - 1$$ with appropriate initial and boundary conditions and with the conditions $$u = 0$$ and $$\partial u/ \partial x = 0$$ on the unknown moving boundary $$x = s(t)$$ is considered, which is like a one-phase Stefan problem but with vanishing latent heat. Such problem models the diffusion of oxygen into an absorbing medium.
An unconditionally stable explicit easily implementable finite difference numerical scheme is presented and tested in the paper. A comparison with results obtained by other methods of other authors is made, the results being similar but calculated here much more effectively.

### MSC:

 65Z05 Applications to the sciences 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 80A22 Stefan problems, phase changes, etc. 35R35 Free boundary problems for PDEs 35K05 Heat equation
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### References:

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