On the grid method for solving the Dirichlet problem for the Laplace equation in a cylinder with lateral surface of class \(C_{1,1}\) (Q2709563)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the grid method for solving the Dirichlet problem for the Laplace equation in a cylinder with lateral surface of class \(C_{1,1}\) |
scientific article |
Statements
21 January 2002
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Dirichlet problem
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grid method
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difference scheme
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Laplace equation
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converge
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On the grid method for solving the Dirichlet problem for the Laplace equation in a cylinder with lateral surface of class \(C_{1,1}\) (English)
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The author constructs and analyzes difference scheme for solving the Dirichlet problem for the Laplace equation in a cylinder with a lateral surface of class \(C_{1,1}\). The uniform convergence of the difference solution with rate \(O(h^2 \ln h)\) is proved, where \(h\) is the grid step size. The requirements on the smoothness of the lateral surface of the cylinder and on the boundary values do not ensure the boundedness of the second derivatives of the solution of the Dirichlet problem.
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