math572_hw1 - MATH 572 Numerical Methods for Scientific...

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Unformatted text preview: MATH 572 Numerical Methods for Scientific Computing II Winter 2005 hw#1 due: Tuesday, January 25 0. Write a brief description of your scientific interests and/or reasons for taking this course. If you work in a lab or research group, please give your supervisors name and describe briefly the project youre working on. (1 paragraph is fine) 1. Consider the problem y = ay + b, y (0) = y , where a, b are constants and a 6 = 0. Find the exact solution y ( t ). Let u n be the numerical solution at time t = nh given by Eulers method. Find an expression for u n and show that lim n u n = y ( t ). 2. Consider the problem y =- y 2 , y (0) = 1. a) Compute y (1) using Eulers method with stepsize h = 0 . 1 , . 05 , . 025 , . 0125. Present the results in a table with the following information. column 1: h column 2: u n column 3: u n- y n column 4: ( u n- y n ) /h b) Find the principal error function E ( t ) and evaluate E (1). Compare with column 4....
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