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A finite difference method for an inverse Sturm-Liouville problem in impedance form

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Abstract

In this paper, the inverse Sturm-Liouville problem for a symmetric impedance is considered and a new iterative method is proposed. Based on the discretization of the Sturm-Liouville operator by a finite difference method, the inverse Sturm-Liouville problem for a symmetric impedance is approximated by a related matrix inverse eigenvalue problem. In solving the matrix inverse eigenvalue problem, the correction technique is discussed to obtain eigenvalues which are close to the finite difference eigenvalues. Then an approximation to the impedance function is achieved by solving the nonlinear equations with modified Newton’s method. Convergence of the method is established and the effectiveness is shown by the numerical experiments.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Hubei University of Education, Wuhan, 430205, China

    Qin Gao

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Zhengda Huang & Xiaoliang Cheng

Authors
  1. Qin Gao
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  2. Zhengda Huang
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  3. Xiaoliang Cheng
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Correspondence to Qin Gao.

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Gao, Q., Huang, Z. & Cheng, X. A finite difference method for an inverse Sturm-Liouville problem in impedance form. Numer Algor 70, 669–690 (2015). https://doi.org/10.1007/s11075-015-9968-7

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  • DOI: https://doi.org/10.1007/s11075-015-9968-7

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