Heun's Method Demo
This demonstration plots the result of using Heun's method for an ordinary differential equation of the form \(y' = f(x, y)\) with initial conditions \(y(x_0) = y_0\).
You can change the following inputs in the demonstration.
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There are three possible types of differential equations that can be used: \[y' = f(x, y) \qquad \text{and} \qquad y' = f(y) \qquad \text{and} \qquad y' = f(x).\] Select the type of differential equation you want via the buttons in the first row; the function \(f\) for each type of differential equation can be entered in a box.
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The interval in the \(x\)-axis on which the function is plotted can be changed by sliders.
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The interval in the \(y\)-axis on which the function is plotted can be changed by sliders.
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The numbers \(x_0\) and \(y_0\) can be changed.
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The step size \(h\) can be changed to any of \(2\), \(1\), \({1 \over 2}\), \({1 \over 5}\), \({1 \over 10}\), \({1 \over 20}\).
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The number of steps \(n\) can be changed.
Using this Demo
To start the demonstration, click on the button "Launch the Demonstration Now."
To change the inputs in the demonstration, note the following.
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When you type something in an input box, the demonstration won't recompute until you hit Return on your keyboard.
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When you drag a slider back and forth, the demonstration won't recompute until you let go of the mouse button.
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There may be a few second delay when the demonstration recomputes, depending on the speed of your internet connection.
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