Computing Eigenvalues of Sturm--Liouville Operators with a Family of Trigonometric Polynomial Potentials

Abstract

We provide estimates for the periodic and antiperiodic eigenvalues of non-self-adjoint Sturm--Liouville operators with a family of complex-valued trigonometric polynomial potentials. We even approximate complex eigenvalues by the roots of some polynomials derived from some iteration formulas. Moreover, we give a numerical example with error analysis.