Titlebook: Numerical Boundary Value ODEs; Proceedings of an In Uri M. Ascher,Robert D. Russell Conference proceedings 1985 Birkh?user Boston, Inc. 198

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The Role of Conditioning in Shooting TechniquesThe aim of the analysis is to deduce convergence of a numerical scheme by establishing the convergence of the scheme when applied to a number of subproblems. Since such an approach is useful only if the subproblems are reasonably well conditioned, the question of conditioning is addressed. It is sho

Inclement

On Non-Invertible Boundary Value Problemsondition numbers and stability do not apply. Such problems typically arise when the interval is semi-infinite. If one assumes that the desired solution is bounded the boundary conditions are sufficient to give a unique solution (as an element of the bounded solutions manifold). Another type of probl

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Discretizations with Dichotomic Stability for Two-Point Boundary Value Problems of fundamental solutions [7], with decaying modes controlled by initial conditions, and growing modes controlled by terminal conditions [10]. It was shown in [3] that it is important for a discretization of such a problem to preserve the dichotomy property, and the implications of this stability cr

Rodent

Improving the Performance of Numerical Methods for Two Point Boundary Value Problems multiple shooting, collocation and other local discretizations can share a common structure. The identification of this common structure permits us to analyse how various components of a method interact and also permits us to consider the assembly of a collection of modular routines which will even

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The Spline-Collocation and the Spline-Galerkin Methods for Orr-Sommerfeld Problemoretical and prac-tical aspects of the spline-collocation method have been examined by R.D.Russell and L.F.Shampine [15] . C. de Boor and B.Swartz [5] have studied a question of choosing the points in the spline-collocation method. They have shown that the greatest rate will be achieved by the choic

小臼

On the Simultaneous Use of Asymptotic and Numerical Methods to Solve Nonlinear Two Point Problems wiordinary differential equations. The aim is to emphasize important and difficult open problems needing much more study, in terms of both mathematical and numerical analysis and computational experiments. The presentation will, regrettably, be removed from both direct applications and substantial ach

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Prologue

A Numerical Method for Singular Perturbation Problems with Turning Pointsas been largely neglected. Indeed, even the analytic study of general systems of first order ODEs with this type of behavior appears to be quite limited; perhaps this is one of the reasons for the lack of progress in this area. In this paper, we report on results obtained with H. O. Kreiss and N. Ni