Abstract

The author and J. Paine [2] showed that the error in the estimates obtained by Numerov's method for the eigenvalues of regular Sturm- Liouville problems with Dirichlet boundary conditions could be dramatically reduced by an asymptotic correction technique studied in [3] in connection with the classical second order finite difference method. In [1] it was shown how the technique could be extended to problems with one or more boundary conditions of the form y'(a) = 0. It was noted in [1] that the implementation of the corrected Numerov method was more difficult for problems involving boundary conditions of the form y'(a) = cy(a) for nonzero c. This paper shows how the method can be implemented in this more difficult case.

References

[1] A.L. Andrew, J. Comp. Appl. Math 125 (2000) 359-366.

[2] A.L. Andrew and J.W. Paine, Numer. Math. 47 (1985) 289-300.

[3] J.W. Paine, F.R. de Hoog and R.S. Anderssen, Computing 26 (1981) 123-139.

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