An improved perturbation technique for eigenvalues of continuous systems

Abstract

AbstractA technique that improves the accuracy of the eigenvalue predictions as computed by a first‐order uniform expansion perturbation scheme for a class of eigenvalue problems associated with linear ordinary and partial differential equations is introduced. As suggested by a comparison with the classical Ritz method, the computational accuracy of a usual perturbation technique such as strained parameters can be effectively increased by simply replacing the usual M‐norms appearing in the denominator of the expressions for the first‐order changes in the eigenvalues by the corresponding MP‐norms, where MP is the perturbed M operator. With increasing sizes of the perturbations of the operators L and M of the class of boundary‐value problems considered, this improved perturbation technique produces results of substantially increased accuracy relative to the usual first‐order uniform expansion perturbation techniques. Numerical examples are presented.