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Solve the system x? + xy3 = 9 3x?y - y' = 4 using Newton's method for nonlinear systems. Use each of the initial guesses (xо, Уo) — (1.2, 2.5), (— 2, 2.5), (-1.2, - 2.5), (2, — 2.5). Observe which root to which the method converges, the number of iterates required, and the speed of convergence.

Solve the system x? + xy3 = 9 3x?y - y' = 4 using Newton's method for nonlinear systems. Use each of the initial guesses (xо, Уo) — (1.2, 2.5), (— 2, 2.5), (-1.2, - 2.5), (2, — 2.5). Observe which root to which the method converges, the number of iterates required, and the speed of convergence.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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51. Solve the system x2 + xy = 9 3x?y - y³ = 4 using Newton's method for nonlinear systems. Use each of the initial guesses (xo, Y) = (1.2,2.5), (-2,2.5), (-1.2, -- 2.5), (2, –2.5). Observe which root to which the method converges, the number of iterates required, and the speed of convergence.
Transcribed Image Text:51. Solve the system x2 + xy = 9 3x?y - y³ = 4 using Newton's method for nonlinear systems. Use each of the initial guesses (xo, Y) = (1.2,2.5), (-2,2.5), (-1.2, -- 2.5), (2, –2.5). Observe which root to which the method converges, the number of iterates required, and the speed of convergence.
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