Euler's method

Consider the initial value problem

whose exact solution is x(t) = 1 + t + tan (t -1).

The applet below solves the problem on interval [1, 2] by Euler's method. Number of steps is 500. The upper line is the numerical solution generated by the applet; the graph below is the error - absolute value of the difference between the numerical and exact solution. As you can see, the error grows as function progresses, because the error is accumulated since function's current value is heavily based on its previous value.