Up to now, we have seen three techniques for reducing the error for solving an initial value problem of the form:

^{(1)}(

*t*) = f(

*t*, y(

*t*) )

y(

*a*) =

*y*

_{0}

where we estimated for y(*b*) with a single step (or iteration).
To get a better answer, use the same strategy as we did for the
composite trapezoidal rule by breaking the interval up into smaller
sub intervals and applying either Euler's, Heun's or the 4th-order
Runge Kutta methods on each subinterval.

# Background

Useful background for this topic includes:

- 4. Linear Algebra
- 14.1 Euler's Method
- 14.2 Heun's Method
- 14.3 4th-Order Runge-Kutta Method

# References

See the corresponding references in the last three background topics.

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