EULER'S METHOD

Select an ODE using the popdown [v] button at lower right. The [Slope Field] key cycles between showing the slope field in thte graphing window in white, grey, or not at all.

Choose a stepsize from the columnn of keys at bottom. Choosing [Actual] will cause an RK4 solution with small stepsize to be drawn; [All Euler] will cause the Euler polygons correspsonding to all four of the Euler stepsizes available to be drawn.

The values of \(x, y,\) and \(F(x,y)\) are read out to the right. Set an initial condition by clicking. The current values of \(x\) and \(y\) are taken as initial conditions and read out as \(x_0\) and \(y_0\) to the right. Rolling the cursor over the graphing window displays the vector \((\hat{i} + F(x,y)\hat{j}) h\) where \(h\) is the step size.

Click on [Start] to begin constructing the Euler polygon. The next segment of the polygon is drawn, the coordinates of the new vertex are displayed at the bottom of the column of values at left, and the button then changes to [Next Step]. Click on [Next Step] to continue the construction of the Euler polygon.

Click on [Clear] to clear everything except for the currently chosen initial condition.

Click on [Zoom] to toggle between two scales.

© 2001 H. Hohn and H. Miller