Heun's method

In mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.

The procedure for calculating the numerical solution to the initial value problem via the improved Euler's method is:

by way of Heun's method, is to first calculate the intermediate value ${\displaystyle {\tilde {y}}_{i+1}}$ and then the final approximation ${\displaystyle y_{i+1}}$ at the next integration point.

where ${\displaystyle h}$ is the step size and ${\displaystyle t_{i+1}=t_{i}+h}$.

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