Question 2: Consider the nonlinear system -x1 + 10x2 – cos(x1 – x2) – 2 = 0 10x, + x2 + sin (x, + x2) – 1 = 0 (a) Find a bounded set Dc R? and a function G: D → R² such that G has a unique fixed-point p' in D that is also a solution to the nonlinear system. (b) Approximate the solution p' to within 10 3 in the loo norm. Use the initial guess (0.036, 0.29)'.
Question 2: Consider the nonlinear system -x1 + 10x2 – cos(x1 – x2) – 2 = 0 10x, + x2 + sin (x, + x2) – 1 = 0 (a) Find a bounded set Dc R? and a function G: D → R² such that G has a unique fixed-point p' in D that is also a solution to the nonlinear system. (b) Approximate the solution p' to within 10 3 in the loo norm. Use the initial guess (0.036, 0.29)'.
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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![Question 2: Consider the nonlinear system
-x1 + 10x2 - cos(x1-x2) - 2 = 0
10x, + x2 + sin (x, + x2) – 1 = 0
(a) Find a bounded set D c R? and a function G: D → R? such that G has a unique fixed-point p' in D that is
also a solution to the nonlinear system.
(b) Approximate the solution p to within 10-3 in the loo norm. Use the initial guess (0.036, 0.29)'.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4ce387a-72a8-466d-9b9c-a59631873abd%2Fb7d976bd-aa4d-499b-960d-86cb330d2c5e%2Fbeqpzzd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 2: Consider the nonlinear system
-x1 + 10x2 - cos(x1-x2) - 2 = 0
10x, + x2 + sin (x, + x2) – 1 = 0
(a) Find a bounded set D c R? and a function G: D → R? such that G has a unique fixed-point p' in D that is
also a solution to the nonlinear system.
(b) Approximate the solution p to within 10-3 in the loo norm. Use the initial guess (0.036, 0.29)'.
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