Abstract:
On the basis of hyperbolic heat conduction equation, the three-layer of compact difference schemes of order 4+2, 4+4 and Saul’ev scheme of order 6+3 are constructed on
minimal three-point stencils in space. À close connection between the explicit Chetverushkin scheme and the three-layer asymptotically stable Samarskii scheme is shown. It is also proposed to combine the classical models of filtration and heat conduction into a
single mathematical model based on the definition of a generalized solution according to
Godunov. The algorithms of order 4+2 obtained in this way are generalized to quasilinear
parabolic equations with arbitrary nonlinearity. Numerical calculations of a number of
test problems are given, illustrating the efficiency of compact schemes.
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