An Euler Pathology
by Mike Martin

On this page, you can vary the number of steps in the Euler's Method approximation to the following initial-value problem:

x ' (t) = 1 - t sin (x (t))
x (0) = 1

The approximation for x (t) using N steps is calculated for the t-interval [0, T ]. Once the parameters are set the page will plot (in red) the approximation to the exact solution (actually the approximation produces only points, but the points are joined by line segments to form the red "curve"). The exact solution is also plotted (in blue). Submit a real, positive, integer value for the parameter N and a real, positive value for the parameter T. Use at your own risk as some parameter values may produce erroneous graphs, but parameters consistent with the literature will work.

Enter in the value of the parameter N, then press the "Plot/Evaluate" button.

N =  

T =  


References:

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