On Rayleigh-Ritz Method in Three-Parameter Eigenvalue Problems

Abstract

paper deals with the computation of the eigenvalues of a three-parameter Sturm-Liouville problem in the form of ordinary differential equation using Rayleigh-Ritz Method, a method which is based on the principle of variational methods. This method has been effective in computing the eigenvalues of self-adjoint problems. The resulting equations obtained in applying Rayleigh-Ritz method on the problem are solved to find the rough estimates of the eigenvalues of the problem. Rough estimates are used as starting approximations in the corresponding shooting method to obtain their actual values. Keywordseigenfunction, multiparameter, variational method, Rayleigh-Ritz method. In this paper a brief account of the method used is given. The starting values of the eigenvalues are obtained by solving the algebraic equations obtained on application of Rayleigh-Ritz method. Using these starting values in the corresponding shooting method of the problem, actual values are obtained. The shooting method requires good starting values because the convergence and its rapidity both depend on starting values. Shooting method of (10) is extended to treat the problem (1.1)-(1.2) numerically in the present case.