From https://en.wikipedia.org/wiki/Heun%27s_method

# Heun’s method

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In mathematics and computational science, **Heun’s method** may refer to the **improved**[1] or **modified Euler’s method** (that is, the **explicit trapezoidal rule**[2]), 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 and then the final approximation at the next integration point.

where is the step size and .