On the validity and stability of the method of lines for the solution of partial differential equations (Q1089770)
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scientific article; zbMATH DE number 4005528
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the validity and stability of the method of lines for the solution of partial differential equations |
scientific article; zbMATH DE number 4005528 |
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On the validity and stability of the method of lines for the solution of partial differential equations (English)
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1987
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The method of lines based on the simplest finite difference replacement of \(\partial^ 2/\partial y^ 2\) is applied to the soluton of the Dirichlet problem for Laplace's equation \(\partial^ 2u/\partial x^ 2+\partial^ 2u/\partial y=0\) in a square in the (x,y)-plane. The standard Fourier series representation of the true and the numerical solutions are given and several perfunctory conclusions are drawn.
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stability
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Laplace equation
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method of lines
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Dirichlet problem
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Fourier series representation
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