h12 - Compare the results with the exact value e=2.71828...

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Ma 449: Numerical Applied Mathematics Reading and Homework Assignment 12 change---> Due: MONDAY, DECEMBER 7th, 2009 Prof. Wickerhauser You are encouraged to collaborate on homework, and to work additional exercises from the indicated problem sections, although the homework grade will be based only on the exercises listed below. Please return your solutions to me by the end of class. LATE HOMEWORK WILL NOT BE ACCEPTED. Check your solutions to problems marked with an asterisk(*) against the values in the textbook's Answers section, pp.646--672. Read Chapter 9, Sections 9.4 to 9.9 of the text. Do Algorithm 13 of Section 9.7, p.526. Problem H12.1. Write a computer program to solve the following initial value problem on the interval [0,1]: y'(t) = 2*t*y(t), 0<t<1; y(0)=1, using the fourth-order Runge-Kutta method. Have the program prompt the user for the number of steps N, then use h=1/N as the step size. Make a table of the values y(1) for N=10, N=100, and N=1000.
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Unformatted text preview: Compare the results with the exact value e=2.71828 18284 59045 23536 02874. ... Problem H12.2. Write a computer program to solve the initial value problem of H12.1, using the Adams-Bashforth-Moulton predictor-corrector method. Use the fourth-order Runge-Kutta method to produce the initial values y_1, y_2, y_3, f_1, f_2, and f_3. Make a table of the values y(1) for N=10, N=100, and N=1000 and compare the results with the exact value e. Problem H12.3. Write a computer program to solve the boundary value problem x''(t) = 2*t*x'(t)/(1+t*t) - 2*x(t)/(1+t*t) + 1; x(0)=1, x(4)=-1, over the interval [0,4]. Use shooting with any method (Euler, Runge-Kutta, Heun, etc.) and a step size of 0.1 to compute a solution. Problem H12.4. Write a computer program to solve the boundary value problem of Problem H13.3 using the finite difference method. Choose h=0.1 and compare the value at t=2 with the one given by the shooting method....
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This note was uploaded on 05/16/2010 for the course MATH 449 taught by Professor Wickerhauser during the Fall '09 term at Washington University in St. Louis.

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