Approximate solution of the Sturm–Liouville problems with Legendre–Galerkin–Chebyshev collocation method

In this paper, we use the Legendre–Galerkin–Chebyshev collocation method (LGCC) to approximate the eigenvalues of a regular Sturm–Liouville problem with three kinds of boundary conditions. Unlike the classical Chebyshev collocation method, this method preserves the symmetry of the problem. Numerical results show that the method is of high accuracy.