Geodesic
A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Neumann’s condition
Commentationes Mathematicae, Tome 49 (2009) no. 1, pp. 83-106.

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

Classical solutions of nonlinear second-order partial differential functional equations of parabolic type with Neumann’s condition are approximated in the paper by solutions of associated explicit difference functional equations. The functional dependence is of the Volterra type. Nonlinear estimates of the generalized Perron type for given functions are assumed. The convergence and stability results are proved with the use of the comparison technique. These theorems in particular cover quasi-linear equations, but such equations are also treated separately. The known results on similar difference methods can be obtained as particular cases of our simple result.
DOI : 10.14708/cm.v49i1.5281
Mots-clés : parabolic differential functional equations, difference methods, nonlinear estimates of the generalized Perron type 
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Lucjan Sapa. A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Neumann’s condition. Commentationes Mathematicae, Tome 49 (2009) no. 1, pp.  83-106. doi : 10.14708/cm.v49i1.5281. http://geodesic.mathdoc.fr/articles/10.14708/cm.v49i1.5281/

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