On symmetric potential in a boundary value problem dependent on an eigenparameter

Abstract

In this work, we asymptotically calculate the eigenvalue of a boundary value problem that involves an integrable and symmetric potential over a defined interval and includes eigenvalues in the boundary conditions. We apply the Riccati equation to derive the asymptotic solutions. To validate our findings, we compare them with numerical results obtained using the element–free Galerkin method. The comparison confirms the consistency and accuracy of the asymptotic approach.