Computation of Some Second Order Sturm-Liouville Bvps using Chebyshev-Legendre Collocation Method

Authors

  • Humaira Farzana Department of Arts & Sciences, Ahsanullah University of Science & Technology Dhaka-1215
  • Md Shafiqul Islam Department of Applied Mathematics, Dhaka University, Dhaka-1000

DOI:

https://doi.org/10.3329/ganit.v35i0.28574

Keywords:

Sturm-Liouville problems, Eigenvalue, Chebyshev nodes, Legendre polynomials, Spectral collocation method

Abstract

We propose Chebyshev-Legendre spectral collocation method for solving second order linear and nonlinear eigenvalue problems exploiting Legendre derivative matrix. The Sturm-Liouville (SLP) problems are formulated utilizing Chebyshev-Gauss-Lobatto (CGL) nodes instead of Legendre Gauss-Lobatto (LGL) nodes and Legendre polynomials are taken as basis function. We discuss, in details, the formulations of the present method for the Sturm-Liouville problems (SLP) with Dirichlet and mixed type boundary conditions. The accuracy of this method is demonstrated by computing eigenvalues of three regular and two singular SLP's. Nonlinear Bratu type problem is also tested in this article. The numerical results are in good agreement with the other available relevant studies.

GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 95-112

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Author Biography

Humaira Farzana, Department of Arts & Sciences, Ahsanullah University of Science & Technology Dhaka-1215



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Published

2016-06-28

How to Cite

Farzana, H., & Islam, M. S. (2016). Computation of Some Second Order Sturm-Liouville Bvps using Chebyshev-Legendre Collocation Method. GANIT: Journal of Bangladesh Mathematical Society, 35, 95–112. https://doi.org/10.3329/ganit.v35i0.28574

Issue

Vol. 35 (2015)

Section

Articles

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The copyright of GANIT: Journal of Bangladesh Mathematical Society is reserved by Bangladesh Mathematical Society (web: https://bdmathsociety.org/)