An improvement for Chebyshev collocation method in solving certain Sturm–Liouville problems

In this paper, the Chebyshev collocation method with an improved step for computing the approximate eigenvalues of regular Sturm–Liouville problems is proposed. The method is investigated for applying to the Sturm–Liouville problems with two points and (semi-)periodic boundary conditions. The new step simplifies the computation by solving a generalized matrix eigenvalue problem instead of solving a high order algebraic equation required by the original method and thus more accurate results can be achieved. The numerical results are encouraging.