On the determination of the roots of some classes of transcendental equations

Abstract A new approach is developed for fast, automatic and accurate computation of the roots of some classes of transcendental equations without the risk of missing any one of the roots. The method permits the calculation of as many eigenvalues as desired or any one of them directly, without the need for computing the previous ones. The computation procedure is based on the count of the number of roots of the transcendental equation lying between zero and some prescribed value in the eigenvalue spectrum. Basic rules in the application of this method are described, and its use for determining the roots of the transcendental equation is illustrated with examples.