Heun's method

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In mathematics and computational science, Heun's method, named after Karl L. W. M. Heun, is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It can be seen as an extension of the Euler method into a two-stage second-order Runge-Kutta method.

The procedure for calculating the numerical solution to the initial value problem

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

[edit] Derivation

The scheme can be compared with the implicit trapezoidal method, but with f(t_{i + 1},y_{i + 1}) replaced by in order to make it explicit. is the result of one step of Euler's method on the same initial value problem.

So, the Heun's method is a predictor-corrector method with forward Euler's method as predictor and trapezoidal method as corrector.

[edit] Runge-Kutta method

Heun's method is a two-stage Runge-Kutta method, and can be written using the tableau

	0
	1	1
		1/2	1/2

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