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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Dong Yun Shen, Department of Mathematics, Foshan University, Foshan, Guangdong, China
Yong Huang, Department of Mathematics, Foshan University, Foshan, Guangdong, China
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.
Dong Yun Shen,
Application Chebyshev Polynomials for Determining the Eigenvalues of Sturm-Liouville Problem, Applied and Computational Mathematics.
Vol. 4, No. 5,
2015, pp. 369-373.
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