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Keywords:
invariant imbedding; singular boundary value problems; linear second order differential equation; method of transfer of conditions; Fourier method; Poisson equation; radial Schrödinger equation; numerical analysis
invariant imbedding; singular boundary value problems; linear second order differential equation; method of transfer of conditions; Fourier method; Poisson equation; radial Schrödinger equation; numerical analysis
Summary:
Numerical solution of linear boundary value problems for ordinary differential equations by the method of transfer of conditions consists in replacing the problem under consideration by a sequence of initial value problems. The method of transfer for systems of equations of the first order with Lebesque integrable coefficients was studied by one of the authors before. The purpose of this paper is to extend the idea of the transfer of conditions to singular boundary value problems for a linear second-order differential equation.
References:
[1] G. H. Meyer: Initial Value Methods for Boundary Value Problems - Theory and Application of Invariant Imbedding. Academic Press, New York 1973. MR 0488791 | 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. In: Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations (A. K. Aziz, ed.), Academic Press, New York-San Francisco- London 1975, pp. 317-330. MR 0405872 | Zbl 0335.65036
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