Geodesic
Difference method for a nonlinear parabolic equation of second order in two space variables
Mathematica Applicanda, Tome 18 (1990) no. 32, pp. 63-78.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

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.
DOI : 10.14708/ma.v18i32.1738
Classification : 65N06 (65N12)
Mots-clés : Finite difference methods, Stability and convergence of numerical methods 
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Roman Kawecki. Difference method for a nonlinear parabolic equation of second order in two space variables. Mathematica Applicanda, Tome 18 (1990) no. 32, pp.  63-78. doi : 10.14708/ma.v18i32.1738. http://geodesic.mathdoc.fr/articles/10.14708/ma.v18i32.1738/

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