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Approximations of Sturm-Liouville eigenvalues using differential quadrature (DQ) method. (English) Zbl 1092.65067

Summary: The polynomial-based differential quadrature and the Fourier expansion-based differential quadrature methods are applied to compute eigenvalues of the Sturm-Liouville problem. It is demonstrated through some examples that accurate results for the first \(k\)th eigenvalues of the problem, where \(k=1,2,3,\dots\), can be obtained by using (at least) \(2k\) mesh points. The results of this work are compared with other published results in the literature.

MSC:

65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators
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