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Using the Accelerated Convergence Method for Solving the Singular Sturm–Liouville Problem

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Abstract

This article is dedicated to the memory of L.D. Akulenko, who worked with the author of the article worked for more than 40 years. Within the framework of the accelerated convergence method developed jointly, a number of classes of problems related to the Sturm–Liouville problems were solved. Based on the research results, several dozen articles and generalizing monograph [1] were published. In this paper, we describe the adaptation of the method to solving singular Sturm–Liouville problems.

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REFERENCES

  1. L. D. Akulenko and S. V. Nesterov, High-Precision Methods in Eigenvalue Problems and Their Applications (Chapman and Hall/CRC Press, Boca Raton, FL, 2005).

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  2. S. G. Ratneswar and Gh. Ranjit, “Method of perturbation applied to the vibration problem of a circular membrane of varying density,” J. Acoust. Soc. Am. 36 (6), 1118–1120 (1964).

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  3. L. N. Sretenskii, The Theory of Fluid Wave Motion (Nauka, Moscow, 1977) [in Russian].

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  4. S. V. Nesterov and V. G. Baidulov, “The way to apply the accelerated convergence method in singular Sturm–Liouville problems,” in Proc. 13th Int. School-Conf. for Young Scientists “Waves and Vortices in Complicated Media” (Moscow, Nov. 30–Dec. 2, 2022), pp. 194–195 [in Russian].

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Funding

The work was carried out within the framework of state order no. 123021700050-1.

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia

    S. V. Nesterov

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  1. S. V. Nesterov
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Correspondence to S. V. Nesterov.

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The author of this work declares that he has no conflicts of interest.

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In loving memory of L.D. Akulenko

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Nesterov, S.V. Using the Accelerated Convergence Method for Solving the Singular Sturm–Liouville Problem. Mech. Solids 58, 2757–2763 (2023). https://doi.org/10.3103/S0025654423080149

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  • DOI: https://doi.org/10.3103/S0025654423080149

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