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Unformatted text preview: Applied Mathematics E2101y Introduction to Applied Mathematics Problem Set #4, due Thursday, 5 March 2009 All references are to Zill & Cullen (3rd edition). Chapter 2, § 2.6: The Euler Method #2 In addition to the two step sizes for h listed, also try to get to the endpoint in just one step: h = 0 . 2. Comment on the quality of the three numerical approximations for y (0 . 2): which do you expect to be best? Chapter 6, § 6.1: The Improved Euler Method #11 Integrate only to x = 0 . 2 in each case. [Hint: For the analytic solution, let u ( x ) = x + y- 1 and derive a separable equation for u ( x ), recalling that R du 1+ u 2 = arctan u .] Chapter 6, § 6.2: The Runge-Kutta Method #1 Integrate only to x = 0 . 2. Chapter 6: Supplementary Problems (a) Consider Euler’s method for y = Ay , y ( x ) = y , where A is a constant, and show that y n = y (1 + Ah ) n . Show that, in the limit as h → 0, the solution of the Euler difference equation approaches the solution of the continuous problem from which it is derived.equation approaches the solution of the continuous problem from which it is derived....
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This note was uploaded on 11/02/2009 for the course APMA 2102 taught by Professor Keyes during the Spring '08 term at Columbia.
- Spring '08