A numerically rigorous proof of curve veering in an eigenvalue problem for differential equations
Parameter-dependent selfadjoint eigenvalue problems for a system of ordinary fourth-order differential equations are considered. The phenomenon of eigenvalue curves veering is investigated by the use of numerical procedures. The author proposes such methods of computing bounds of the form \[ p(\Omega)-\epsilon \leq \lambda(\Omega) \leq p(\Omega)+\epsilon \] for the eigenvalue curves \(\lambda(\Omega)\) that rounding errors are rigorously controlled by the use of interval arithmetic. By means of calculated bounds, the phenomenon of curve veering for a concrete situation can be proved without requiring special properties of the eigenvalue curves.
parameter-dependent selfadjoint eigenvalue problems
systems of ordinary fourth-order differential equations
scientific article; zbMATH DE number 856812
scientific article