ps4solutions[1]

ps4solutions[1] - APMA 2101 Problem Set#4 Sample Solution...

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APMA 2101 Problem Set #4 Sample Solution Set (due 5 March 2009) Section 2.6.: The Euler Method (5 pts] Trying to get to the endpoint in just one step, h= 0.2, is trivial, y (0.2)=0. Of course, we expect the finest mesh step h =0.05 to be best, since all calculations use a method of the same fixed order. Section 6.1: The Imrpoved Euler Method [5 pts] 11. The exact solution, following the hint, is u(x) = tan(x+c) , or with the initial condition and a return to the original variables, y(x)=tan(x+ π /4)+1-x . Section 6.2: The Runge-Kutta Method [4 pts] Chapter 6: Supplementary Problems [4 pts (2 pts each)] (a) The solution of y’=Ay with y(0)=y 0 is y(t)=y 0 exp(At) , so y(t n )=y 0 exp(At n ), where t n =nh. The limit of the binomial expansion
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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.

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ps4solutions[1] - APMA 2101 Problem Set#4 Sample Solution...

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