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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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S6)Please answer in legible and clear handwriting.

6) Three approximations (x;-2, Yi-2), (xi-1, Yi–1) and (xi, y;) to the solution of
the nonlinear system f1(x, y) = 0 and f2(x, y) = 0 are considered. Defining two
planes using these three points with the following definition for zi-k:
Zi–k = f;(xj-k; Yi–k)
j = 1, 2; k = 0, 1, 2;
and assuming fi(x, y) = x² + y² – 1 and f2(x, y) = x² – y with three approxi-
mations (2,2), (2,1) and (1,2):
(a) calculate the next approximation (x;+1, Yi+1) by intersecting these two
planes and the z-plane.
(b) compare the error of new approximation with the previous steps.
Transcribed Image Text:6) Three approximations (x;-2, Yi-2), (xi-1, Yi–1) and (xi, y;) to the solution of the nonlinear system f1(x, y) = 0 and f2(x, y) = 0 are considered. Defining two planes using these three points with the following definition for zi-k: Zi–k = f;(xj-k; Yi–k) j = 1, 2; k = 0, 1, 2; and assuming fi(x, y) = x² + y² – 1 and f2(x, y) = x² – y with three approxi- mations (2,2), (2,1) and (1,2): (a) calculate the next approximation (x;+1, Yi+1) by intersecting these two planes and the z-plane. (b) compare the error of new approximation with the previous steps.
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