FD-method for Sturm-Liouville problem with boundary value conditions of the third kind (Q2703299)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | FD-method for Sturm-Liouville problem with boundary value conditions of the third kind |
scientific article |
Statements
1 March 2001
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algorithm
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Sturm-Liouville problem
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boundary value conditions of the third kind
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Pruess method
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convergence
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finite difference method
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FD-method for Sturm-Liouville problem with boundary value conditions of the third kind (English)
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The author considers the boundary value problem NEWLINE\[NEWLINEu''(x)+[\lambda-q(x)]u(x)=0, \;x\in (0,1), \quad u'(0)=\alpha u(0),\;u'(1)=-\beta u(1), \quad \alpha,\beta\geq 0,NEWLINE\]NEWLINE where \(q(x)\geq 0\) is a given piecewise smooth function. The Pruess method is used for approximation of solution of the given problem. A theorem on the rate of convergence of the finite difference (FD) method is proved and an algorithmic implementation of the FD-method is presented.
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