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)'.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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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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