An efficient numerical technique for estimating eigenvalues of second-order non-self-adjoint Sturm–Liouville problems.

This paper investigates the numerical approximation of the eigenvalues of regular and singular second-order non-self-adjoint Sturm–Liouville problems using an efficient technique based on the Chebyshev spectral collocation scheme. For this purpose, the spectral differentiation matrices are used to determine the derivatives of Chebyshev polynomials at the grid points and, then convert non-self-adjoint problem into a generalized eigenvalue problem. The convergence associated with this technique has been discussed. Numerical simulations have been conducted to illustrate the excellent performance of this technique and to demonstrate that it is achieving high accuracy and is computationally cost-effective. Numerical results and comparison with other techniques are presented. [ABSTRACT FROM AUTHOR]