math. sci. appl. e-notes Mathematical Sciences and Applications E-Notes 2147-6268 Murat TOSUN 10.36753/mathenot.1110497 Mathematical Sciences Matematik Computing Eigenvalues of Sturm--Liouville Operators with a Family of Trigonometric Polynomial Potentials https://orcid.org/0000-0001-7375-3474 Nur Cemile Yalova University 03 28 2023 11 1 29 42 04 28 2022 08 02 2022 Copyright © 2013, Mathematical Sciences and Applications E-Notes 2013 Mathematical Sciences and Applications E-Notes

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.

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