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In contrast to the explicit Euler method , the approximation is made using a trapezoid and not a rectangle.
Procedure
To the numerical solution of the initial value problem:
for an ordinary differential equation using Heun's method, choose a discretization step size
, consider the discrete times
and calculate first analogously to the explicit Euler method
and then
what can be formed
The are the approximate values of the actual solution function at times .
is called the step size. If the step size is reduced, the procedural error becomes smaller (i.e., they are closer to the actual function value ). The global error of Heun's method is almost zero; one also speaks of the convergence order 2.