10.1007/s40096-021-00412-6

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

  • Mohamed El-Gamel*1,
  • Waleed Adel1,
  • M. S. El-Azab1,
  1. Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Mansoura, EG

Published in Issue 2021-05-21

How to Cite

El-Gamel, M., Adel, W., & El-Azab, M. S. (2021). Eigenvalues and eigenfunctions of fourth-order sturm-liouville problems using Bernoulli series with Chebychev collocation points. Mathematical Sciences, 16(1 (March 2022). https://doi.org/10.1007/s40096-021-00412-6
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Abstract

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.

Keywords

  • Bernoulli matrix,
  • Eigenvalue,
  • Eigenfunctions,
  • Sturm-Liouville

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