On the numerical solution of the equation \(\frac{\partial ^ 2z\partial ^ 2z}{\partial x^ 2\partial y^ 2}-(\frac{\partial ^ 2z}{\partial x\partial y})^ 2=f\) and its discretizations. I. (English) Zbl 0659.65116

For a bounded convex domain, nonnegative f and Dirichlet data a special discretization of the indicated of the title equation is constructed. For the discrete version of the problem an iterative method that produces a monotonically convergent sequences is proposed. Several numerical examples are presented.
Reviewer: L.G.Vulkov


65Z05 Applications to the sciences
35Q99 Partial differential equations of mathematical physics and other areas of application
65N06 Finite difference methods for boundary value problems involving PDEs
65G30 Interval and finite arithmetic
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