Variations of Eigenvalues and Eigenfunctions in Continuum Mechanics

the corresponding published values in Ref. 4 by less than 5 in the fourth decimal place at each of the 36 tabulated points with the calculated value /(0) = 1.2326740 as compared with 1.232588. The sample calculations other than for the case of /? = 1 were carried out for the cases of /? = 0.5 and 0 using the same initial approximations and the same values of rje, h and & as for the case of /? = 1. The converged solutions were obtained after 4 and 8 iterations, respectively. Unfortunately, the present method cannot be applied to a problem in which the uniqueness of the solution is not assured. For such a problem, special account of the asymptotic behavior of the solution at the outer edge of the boundary layer must be taken and an improved version of quasi-linearization by Libby and Chen seems to be the best of the existing methods. The present method, despite the restriction, seems to provide another useful technique for treating the two-point boundary value problem and is also applicable to the numerical analysis of nonsimilar flows by a difference-differential scheme, such as has been developed by Smith and Clutter.