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Eigenvalues and eigenfunctions of fourth-order sturm-liouville problems using Bernoulli series with Chebychev collocation points

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Abstract

A collocation method based on Bernoulli polynomial is developed to compute the eigenvalues and eigenfunctions of some known fourth-order Sturm-Liouville problems. Properties of Bernoulli matrix method are presented to convert the problem into a system of linear algebraic equations. Error estimation is introduced. The eigenfunctions are calculated for the test problems. A comparison is made with other relevant studies.

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Authors and Affiliations

  1. Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Mansoura, Egypt

    Mohamed El-Gamel, Waleed Adel & M. S. El-Azab

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  1. Mohamed El-Gamel
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  2. Waleed Adel
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  3. M. S. El-Azab
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Correspondence to Mohamed El-Gamel.

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El-Gamel, M., Adel, W. & El-Azab, M.S. Eigenvalues and eigenfunctions of fourth-order sturm-liouville problems using Bernoulli series with Chebychev collocation points. Math Sci 16, 97–104 (2022). https://doi.org/10.1007/s40096-021-00412-6

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  • DOI: https://doi.org/10.1007/s40096-021-00412-6

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