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Generalized difference methods for a nonlinear Dirichlet problem. (English) Zbl 0626.65091

The nonlinear problem studied is \(-\Delta (a(x,y,u)\Delta u)=f(x,y)\) in a domain D, \(u(x,y)=0\) on \(\partial D\), where D is a bounded domain, a is twice continuously differentiable with bounded derivatives through the second order. Generalized difference methods are defined, the existence of the approximate solution is established as is the error estimate for the approximate solution.
Reviewer: W.Ames

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
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