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Difference method for a nonlinear parabolic equation of second order in two space variables

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Kawecki R.

Mathematica Applicanda

1990

tom 18

nr 32

A.C. Reynolds in his paper (1972) proposed a difference parametric method for solving the Fourier problem for a nonlinear parabolic equation of second order in one space variable. The paper presents a generalization of Reynolds’ method for the problem in two space variables with mixed derivatives. In this paper, Fourier problems for a general class of nonlinear parabolic equation, in QT = Q x [0, T], are studied. To solve this problem we construct a finite difference scheme with a real parameter. We prove that the solutions of certain associated finite difference equations are unique and converge to the solution of the initial-boundary value problem with 0(h^2) rate of convergence.

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1 Mathematica Applicanda

1 Kawecki R.

1 1990

Wyniki wyszukiwania

Difference method for a nonlinear parabolic equation of second order in two space variables