Refinement of approximate solutions to a boundary-value problem on a half-line
type: Item
instance of: scholarly article
title: Refinement of approximate solutions to a boundary-value problem on a half-line
zbMATH Open document ID: 0946.65059
author: E. P. Zhidkov
author: A. G. Soloviev
published in: Computational Mathematics and Mathematical Physics
publication date: 2000-07-04T00:00:00Z
review text: The authors consider the refinement of approximate solutions to a boundary value problem for a second-order ordinary differential equation on a half-line. To solve the problem numerically, \([x_{0},\infty)\) is replaced by \([x_{0},R]\), and the boundary condition at \(R\) is derived from the asymptotic form of the solution at infinity. Then, the problem is solved on the segment. The replacement leads to an error. A method for refining approximate solutions to the boundary value problem on a half-line is suggested. The problem is solved for two segments of different length. A refined solution is obtained by extrapolating the solutions obtained along the segment.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 1467920
zbMATH Keywords: extrapolation
zbMATH Keywords: refinement of approximate solutions
zbMATH Keywords: boundary value problem
zbMATH Keywords: second-order ordinary differential equation
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1467920