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Unformatted text preview: 640:244 FALL 2009 Lab 2: Numerical Methods This Maple lab is closely based on earlier versions prepared by Professors R. Falk and R. Bumby of the Rutgers Mathematics department. Introduction. In this lab, we shall use Maple’s ability to approximate the solution of differential equations by numerical methods and add these solutions to the direction fields that we studied in Lab 1. This allows us to extend our understanding of the solutions of differential equations to equations for which a closed form solution is not available. Please obtain the seed file from the web page and save it in your directory on eden, then prepare the Maple lab according to the instructions and hints in the introduction to Lab 0. Turn in only the printout of your Maple worksheet, after removing any extraneous material and any errors you have made. Setup. As usual, the seed file begins with commands which load the required Maple packages: with(plots): and with(DEtools): . Equation 1. a. One Solution. The sequence of commands to begin working with Equation 1 have already been entered into the seed file. Execute them to see how Maple can be used to plot the direction field along with the particular solution satisfying this differential equation and the initial condition y (0) = 0. The quantities x1int and y1int are introduced to have standard names for the ranges of the variables in all graphs in this problem. For the other exercise, corresponding commands can be constructed by copying lines to different places in a worksheet and doing some minor editing. de1:= diff(y(x),x) = 1+ 2*x*y(x) initval1a:={[y(0)=0]}; x1int:=x=2..2;y1int:=y=3..3; DEplot(de1, y(x), x1int, initval1a,y1int,title="Default view of equation 1"); The DEplot command has many options which you can read about in the Maple help pages. Incommand has many options which you can read about in the Maple help pages....
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 Fall '09
 Ming
 Optimization

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