hw6 - y (0) = 1 and y (0) = 0, solve the following initial...

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Numerical Analysis in Engineering ME 140A, Fall 2007 Homework #6 Due: Thursday Dec 6, 8 am. November 29, 2007 1. (35 Points) Solve the following problem over the interval from x = 0 to x = 1 using step sizes of Δ x =0.5, 0.25, 0.1, 0.05 and 0.025. Plot all your results ( y vs x ) for Δ x = 0 . 025 on the same gragh. Then, plot the relative error for y (1) vs Δ x on the logarithmic-scale graph. Discuss the order of accuracy of each method. dy dx = (1 + 2 x ) y, y (0) = 1 . (1) a) Analytically b) Using Euler’s method c) Using Henn’s method without iteration d) Using the fourth order Runge-Kutta method 2. (35 Points) Given the initial conditions
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Unformatted text preview: y (0) = 1 and y (0) = 0, solve the following initial value problem from t = 0 to 4: d 2 y dt 2 + 9 y = 0 (2) Obtain your solutions with: a) Eulers method and b) the fourth order Runge-Kutta method, with step sizes of t = 0.1, 0.05 and 0.01. Plot the solutions on the same graph along with the exact solution y = cos 3 t . Discuss the accuracy of the methods. 3. (30 Points) For the equation dy dt = f ( t ), compare the predictor-corrector method with the Taylor series. Show that the local truncation error is O ( h 3 )....
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This note was uploaded on 11/05/2009 for the course ME 140A taught by Professor Meiburg during the Fall '08 term at UCSB.

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