Topic 14.2: Heun's Method

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The trapezoidal rule ½(f(a) + f(b))(b - a) for integration is much better than using only the left end-point with a formula like f(a)(b - a) because it samples the value of the function at two points. If the function is reasonably smooth, then the interpolation of these two points is appropriate. Similarly, Euler's method only samples the slope at the left end-point, that is, the initial point (t0, y0). Heun's method is an attempt to use information about the slope at both end points to find the average slope.

Like Euler, the eu in Heun sounds like oi, that is, Heun rhymes with coin.

Background

Useful background for this topic includes:

References

Interactive Maplet

A Demonstration of Heun's Method

Copyright ©2005 by Douglas Wilhelm Harder. All rights reserved.