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 (Q1112573)
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scientific article; zbMATH DE number 4078715
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | 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 |
scientific article; zbMATH DE number 4078715 |
Statements
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)
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1988
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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.
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Monge-Ampère equation
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parallel computation
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iterative method
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numerical examples
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