Using the Galerkin method to compute the eigenvalues and eigenelements of the second-order Sturm–Liouville problems
Mokhtar, O., Abbas, W., Fathy, M., A. M. Saidb,, A., ahmed mohammed abd-EL Gawad, H. (2019). Using the Galerkin method to compute the eigenvalues and eigenelements of the second-order Sturm–Liouville problems. EKB Journal Management System, 163(0), 27-42. doi: 10.21608/erj.2019.122499
omar Mokhtar; wael Abbas; Mohamed Fathy; Ahmed A. M. Saidb,; Hesham ahmed mohammed abd-EL Gawad. "Using the Galerkin method to compute the eigenvalues and eigenelements of the second-order Sturm–Liouville problems". EKB Journal Management System, 163, 0, 2019, 27-42. doi: 10.21608/erj.2019.122499
Mokhtar, O., Abbas, W., Fathy, M., A. M. Saidb,, A., ahmed mohammed abd-EL Gawad, H. (2019). 'Using the Galerkin method to compute the eigenvalues and eigenelements of the second-order Sturm–Liouville problems', EKB Journal Management System, 163(0), pp. 27-42. doi: 10.21608/erj.2019.122499
Mokhtar, O., Abbas, W., Fathy, M., A. M. Saidb,, A., ahmed mohammed abd-EL Gawad, H. Using the Galerkin method to compute the eigenvalues and eigenelements of the second-order Sturm–Liouville problems. EKB Journal Management System, 2019; 163(0): 27-42. doi: 10.21608/erj.2019.122499

Using the Galerkin method to compute the eigenvalues and eigenelements of the second-order Sturm–Liouville problems

Engineering Research Journal
Article 3, Volume 163, Issue 0, September 2019, Page 27-42  XML PDF (593.64 K)
Document Type: Original Article
DOI: 10.21608/erj.2019.122499
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Authors
omar Mokhtar* 1; wael Abbas2; Mohamed Fathy2; Ahmed A. M. Saidb,1; Hesham ahmed mohammed abd-EL Gawad1
1Physics and Engineering Mathematics Department, Faculty of Engineering, Mattaria, Helwan University, Egypt.
2Basic and Applied Science Department, College of Engineering and Technology, Arab Academy for Science, Technology, and Maritime Transport, Cairo, Egypt.
Abstract
 
In this paper, an efficient method based on the Galerkin technique for computing the eigenvalues and eigenfunctions for the second-order Sturm-Liouville problems. The first kind of Chebyshev polynomials ( ) is used as basis functions to solve this problem. The Chebyshev-Galerkin method is applied to reduce an ordinary differential equation into a system of algebraic equations using the orthogonality of Chebyshev polynomials and new relations driven from the orthogonality property. Numerical examples show that the proposed method is an easy method to implement and introduce accurate results.
Keywords
Chebyshev; Galerkin; Eigenvalues; Eigenfunctions; Sturm-Liouville
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