Accurate Numerical Approximations of Eigenfrequencies and Eigenfunctions of Elliptic Membranes

In earlier papers [3, 4] a defect‐minimization method was proposed to compute approximate eigenfunctions of membranes by means of a parametric semi‐infinite optimization problem. The method gives approximations and error bounds of eigenvalues and eigenfunctions. An algorithm based on this method has been implemented for the special case of elliptic membranes with variable eccentricity. In this paper we show that by this method we obtain very accurate results even for eccentricities near one. In addition the method is very appropriate to study the behavior of eigenfunctions.