An Euler Machine

Following is a series of "execution groups" consisting of Maple commands. The groups are prefaced by a square brace, and placing the cursor anywhere inside the group and pressing Enter will cause all commands in the group to be executed.

To solve dy/dx = f(x,y) numerically by Euler's method:

First define your right hand side: Replace the "x+y" by your right hand side. Do not delete anything else, including semicolon -- Maple needs this. When finished, put the cursor anywhere in this block (which consists of the single line following) and press Enter. This tells Maple what the definition of f(x,y) is, and you should see that displayed.

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Next define your initial condition and limits: This tells Maple that y(x0) = y0. Also, remember that the final value of x for which Euler's method calculates the approximate y(x) is h*N, so if you change the stepsize h, be sure to adjust the number of steps, N. E.g, to start at x=0 and finish at x=2 with step size h = 0.4, set x0 = 0.0, h = 0.4 and N = 5. When finished with the next block, put the cursor anywhere inside it and press Enter. Your values will be displayed.

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Now do the Euler loop and store your results: You do not have to change anything here. Just put the cursor inside this block and press Enter. The only thing that will display is the first value of x and y.

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Then plot your results: Press Enter with the cursor inside this next block if you want to see a "dot-to-dot" of your computed solution.

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This cell will only print the last computed pair (x,y). If you want to see all of them, change "from N by 1 to N" to "from 1 by 1 to N". Then press Enter with the cursor inside this block to see the outputs of your Euler method calculation.

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