h 2 -EXTRAPOLATION IN EIGENVALUE PROBLEMS
Michael Robert Osborne · The Quarterly Journal of Mechanics and Applied Mathematics · 1960
It is a common hypothesis that the error involved in a certain numerical process is an analytic function of a parameter which specifies in some way the closeness of the approximations used. We consider this hypothesis in detail for difference approximations to differential equation eigenvalue problems. Our approach is to construct the solution of this difference equation by determining a recurrence for the terms in its Taylor series. Existence is then guaranteed by the convergence of this series. The solution thus obtained is used as the basis for a discussion of methods by which h-2-extrapolation of the eigenvalues and eigenvectors of the difference equation could be obtained.