Finite-difference approximation of the boundary conditions of the second and third order for the nonlinear heat conduction equation

2 responses

  1. Daniel Duffy

    Friendly remark,
    The formulae do look very readbable and are non-standard.

    I miss how the paper linearises the nonlinear PDE and the issue of (conditional) stability. Do you have numerical experiments for this problem?

  2. Yury

    Dear Daniel, these non-standard-looking formulae are obtained via the approach, described in "The Theory of Difference Schemes" by Alexander A. Samarski, pp. 82 -- 84.
    The equation is linearized in the usual way (for explicit finite-difference schemes): one takes the values of temperature-dependent coefficients from the previous time level. The stability issue is managed using sufficiently small time step (see method of frozen coefficients).
    As for numerical experiments, we have carried out a lot. The results show that for thin space grids the described boundary condition approximation (of second order in space) is much more effective than the simple one (of first order).

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