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Convergence of Numerov’s method for inverse Sturm-Liouville problems. (English) Zbl 1411.65099
Summary: In this paper, we discuss the convergence of Numerov’s method in [A. L. Andrew, Inverse Probl. 21, No. 1, 223–238 (2005; Zbl 1070.34018); ibid. 22, No. 6, 2069–2081 (2006; Zbl 1114.34011)] for computing Sturm-Liouville potentials from the given eigenvalues. By using the asymptotic estimate for the eigenvalue of the Sturm-Liouville problem and the error in the finite difference eigenvalue, convergence of Numerov’s method for symmetric potentials is proved. Based on the method of symmetric extension, we establish a convergence result of Numerov’s method for the nonsymmetric potential from two spectra. Numerical examples are reported to confirm the theoretically predicted convergence.
MSC:
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
65L09 Numerical solution of inverse problems involving ordinary differential equations
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