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

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