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In order to use Matlab routines for the Euler, Improved Euler and Runge-Kutta Methods, you will need the files eul.m, rk2.m and rk4.m , respectively. These files are already present on all PUCC machines as standard software. If you are using your own copy of Matlab you may need to download these files. Here is a link : dfield/ You must first create a function file in the same directory (or folder) as your Matlab . Here is one way. After Matlab has been opened, pull down the File menu and select “ New M-File ”. A window will pop up for you to create your function file. For example, to create a function file for the function f ( t,y )=6 t 3 - e 2 y + t y ,type: function W=fcn1(t,y) W=6*t 3-exp(2*y)+sqrt(t)/y; (Don’t forget the “ ; ” at the end.) Save this file as a .m file with the SAME name as your function. The above example would be saved as “ fcn1.m ”. You can check if your function has
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Unformatted text preview: been saved by typing something like the following at a Matlab prompt: >> fcn1(1,3) You should get the value of f (1 , 3). • Your initial value problem will have the form : y = f ( t,y ) y ( t ) = y . Assuming f ( t,y ) was saved as the file fcn1.m , the syntax for eul (as well as rk2 and rk4 , just replace eul ) will be : eul(’fcn1’,[t ,t f ],y ,h) where t and t f are the initial and final values of t and h = step size . (Your version of Matlab may not utilize brackets. Type help eul to find out.) To approximate the actual solution to the IVP at t f , with given h , using eul , just type the following at a Matlab prompt: >> [t,y]=eul(’fcn1’,[t ,t f ],y ,h); The approximations y ,y 1 ,y 2 ,...,y n are stored in the matrix y . To print them out type : [t,y] To plot them, type : plot(t,y)...
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