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On the Region of Convergence of Picard's Iteration
Author(s) -
van de Craats J.
Publication year - 1972
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19720520806
Subject(s) - mathematics , convergence (economics) , lipschitz continuity , boundary value problem , fixed point iteration , mathematical analysis , fixed point , economics , economic growth
A new convergence condition is described for Picard's iteration for the boundary value problem\documentclass{article}\pagestyle{empty}\begin{document}$$ y''(t)\; + \;f(t,\;y(t),\;y'(t))\; = \;0,\;y(a)\; = \;A,\;y(b)\;B $$\end{document}where f(t, y, z) is continuous and satisfies a Lipschitz‐condition in y and z. This convergence condition is optimal in a sense specified precisely in this paper.