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High precision results for a two-point boundary value problem

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
6
Issue
2
Identifiers
DOI: 10.1016/0771-050x(80)90003-0

Abstract

Abstract In this note we establish results of high accuracy for the two-point boundary value problem 1. (1a) y″ = n sinh ny with the boundary conditions 2. (1b) y (0) = 0, y (1) = 1, where n is real and positive. At the same time a derivation of the approximation for large n 3. (2) y′(0) = 8 e −n(1 − 2e −n/2 + 2e −n), which is deduced in [1] from numerical results, is obtained in the course of the development.

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