boundary value conditions of the third kind
FD-method for Sturm-Liouville problem with boundary value conditions of the third kind
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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