Newton-Ralphson method (No code submission for this problem). The argument in sin x is radian. The...
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Newton-Ralphson method (No code submission for this problem). The argument in sin x is radian. The nonlinear eqn. e sinx+0.2 has two solutions (roots) in the interval of 0<x<5. We wish to use Newton-Ralphson (NR) method to find these two roots within this interval. In the following, if the method fails to produce a root in the interval, discuss the cause and how to make the method to work. (a) Use Newton-Ralphson (NR) method, with initial guess x=1.0 to find one approximate root by performing 2 iterations. Also compute the relative percentage error for each iteration (5 points); (b) Change the initial guess to x = 3.0 and repeat the calculations as in (b) (5 points); (c) Change the initial guess to x₁ =1.75 and repeat the same calculations. Discuss the results (5 points). (d) Using the MATLAB code provided in the textbook to find the roots: the relative percentage error must be equal to or smaller than 2%. Explore how the choice of the initial guess affects the solution (root) in the interval of 0<x<5, with the following 5 different initial guesses: x₁=0.5,1.5,3.1.,3.5,4.7. Should you check the value f'(x), and why? (10 points). Newton-Ralphson method (No code submission for this problem). The argument in sin x is radian. The nonlinear eqn. e sinx+0.2 has two solutions (roots) in the interval of 0<x<5. We wish to use Newton-Ralphson (NR) method to find these two roots within this interval. In the following, if the method fails to produce a root in the interval, discuss the cause and how to make the method to work. (a) Use Newton-Ralphson (NR) method, with initial guess x=1.0 to find one approximate root by performing 2 iterations. Also compute the relative percentage error for each iteration (5 points); (b) Change the initial guess to x = 3.0 and repeat the calculations as in (b) (5 points); (c) Change the initial guess to x₁ =1.75 and repeat the same calculations. Discuss the results (5 points). (d) Using the MATLAB code provided in the textbook to find the roots: the relative percentage error must be equal to or smaller than 2%. Explore how the choice of the initial guess affects the solution (root) in the interval of 0<x<5, with the following 5 different initial guesses: x₁=0.5,1.5,3.1.,3.5,4.7. Should you check the value f'(x), and why? (10 points).
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a Using the NewtonRaphson method with initial guess x10 we have Iteration 1 x1 x0 fx0fx0 10 sin10 02 cos10 0898951 Relative percentage error x1 x0x1 100 0898951 100898951 100 1169 Iteration 2 x2 x1 fx... View the full answer
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