Abstract
Consider a linear ordinary differential equation of the 2nd order which has a singularity at the origin; according to the nature of this singularity we must consider either the two-point boundary-value problem or the one-point boundary value problem. Finite-difference schemes are studied; results are given concerning error analysis and monotone convergence.
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Forsythe, G., Wasow, W.: Finite-difference methods for partial differential equations. New York: Wiley 1960.
Jamet, P.: Numerical methods and existence theorems of singular linear boundary-value problems. Doctoral Thesis, University of Wisconsin 1967.
—— Numerical methods and existence theorems for parabolic differential equations whose coefficients are singular on the boundary. Maths. of Comp.22, 104, 721–743 (1968).
—— Parter, S. V.: Numerical methods for elliptic differential equations whose coefficients are singular on a portion of the boundary. SIAM Journal, Series B4, 131–146 (1967).
Parter, S. V.: Numerical methods for generalized axially symmetric potentials. SIAM Journal, Series B2, 500–516 (1965)
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The material of this paper is taken from the author's doctoral thesis [2]. The author is greatly indebted to his adviser S. V. Parter. - Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-31-124-ARO-D-462.
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Jamet, P. On the convergence of finite-difference approximations to one-dimensional singular boundary-value problems. Numer. Math. 14, 355–378 (1970). https://doi.org/10.1007/BF02165591
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DOI: https://doi.org/10.1007/BF02165591