Application Chebyshev Polynomials for Determining the Eigenvalues of Sturm-Liouville Problem
Applied and Computational Mathematics
Volume 4, Issue 5, October 2015, Pages: 369-373
Received: Aug. 31, 2015; Accepted: Sep. 11, 2015; Published: Sep. 22, 2015
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Authors
Dong Yun Shen, Department of Mathematics, Foshan University, Foshan, Guangdong, China
Yong Huang, Department of Mathematics, Foshan University, Foshan, Guangdong, China
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Abstract
This paper discusses the eigenvalue problem of second-order Sturm-Liouville equation. We transform the governing differential equation to the Fredholm-Volterra integral equation with appropriate end supports. By expanding the unknown function into the shifted Chebyshev polynomials, we directly get the corresponding polynomial characteristic equations, where the lower and higher-order eigenvalues can be determined simultaneously from the multi-roots. Several examples of estimating eigenvalues are given. By comparison with the exact results in open literatures, the correctness and effectiveness of the present approach are verified.
Keywords
Sturm-Liouville Problem, Eigenvalues, Fredholm-Volterra Integral Equation, Chebyshev Polynomials
To cite this article
Dong Yun Shen, Yong Huang, Application Chebyshev Polynomials for Determining the Eigenvalues of Sturm-Liouville Problem, Applied and Computational Mathematics. Vol. 4, No. 5, 2015, pp. 369-373. doi: 10.11648/j.acm.20150405.16
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