Heun's method

Heun's method is a numerical procedure for solving ordinary differential equations with a given initial value. The name may refer to the improved or modified Euler method, which is the explicit trapezoidal rule, or to a similar two-stage Runge-Kutta method, and it is named after Karl Heun. Both variants can be seen as extensions of the Euler method into two-stage, second-order Runge-Kutta methods. To advance one step, the method first calculates an intermediate value at the next integration point and then computes the final approximation there from it, which corrects the plain Euler step by averaging slopes at the two ends of the step.