Show that the homotopy G(, x) = F(x) e F(x(0)) used in the continuation method with

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Show that the homotopy
G(λ, x) = F(x) − e−λ F(x(0))
used in the continuation method with Euler's method and h = 1 also duplicates Newton's method for any x(0); that is, with x(0) = x(0), we have x(1) = x(1).

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Numerical Analysis

ISBN: 978-0538733519

9th edition

Authors: Richard L. Burden, J. Douglas Faires

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Question Posted: Mar 22, 2016 03:08 AM

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Show that the homotopy G(, x) = F(x) e F(x(0)) used in the continuation method with

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For each we have So And Thus 0 G2 x2 Fx eFx0 ...View the full answer

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