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Transfer of conditions for singular boundary value problems. (English) Zbl 0685.65078

The paper is dealt with the method of transfer of conditions for solving singular boundary value problems for a linear second order differential equation. The method consists in replacing the problem by a sequence of initial value problems.
After a description of the method of transfer of conditions in the regular case, developed by the second author (Rozpravy Ceskosl. Akad. Ved., R. Mat. Prirod. Ved. 83, No.5, 1-134 (1973; Zbl 0276.34009)], the authors present and prove two theorems for the transferred conditions in the singular case. On the basis of these theorems the algorithm for solving singular boundary value problems for a linear differential equation of the second order can be developed easily.
Singular boundary value problems for the considered equation occur in a number of physical problems, e.g. when using the Fourier method for the Poisson equation in polar coordinates, and when solving the eigenvalue problem for the radial Schrödinger equation.
Reviewer: A.Marciniak

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics

Citations:

Zbl 0276.34009
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References:

[1] G. H. Meyer: Initial Value Methods for Boundary Value Problems - Theory and Application of Invariant Imbedding. Academic Press, New York 1973. · Zbl 0304.34018
[2] J. Taufer: Lösung der Randwertprobleme für Systeme von linearen Differentialgleichungen. Rozpravy ČSAV 83 (1973), No. 5. · Zbl 0276.34009
[3] J. Taufer: Numerical Solution of Boundary Value Problems by Stable Methods Based on the Transfer of Conditions. Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations (A. K. Aziz, Academic Press, New York-San Francisco- London 1975, pp. 317-330. · Zbl 0335.65036
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