http://www.ck12.org Chapter 7. Integration Techniques
The Runge-Kutta methods are an important family of implicit and explicit iterative methods for the approximation
of solutions of our ODE. On them, apply Simpson’s rule:
yn+ 1 −yn=∫xn+ 1
xn f′(x)dx=∫xn+h
xn f′(x)dx≈h 6{
y′(xn)+ 4 y′(
xn+h 2)
+y′(xn+ 1 )}
.
Exercise 1.Apply the Euler’s, improved Euler’s and the Runge-Kutta methods on the ODE
dydx=yto approximate the solution that satisfyy( 0 ) =1 fromx=0 tox=1 withh= 0 .2.
We know the exact solution isy=ex. Compare their relative accuracy against the exact solution.
Texas Instruments Resources
In the CK-12 Texas Instruments Calculus FlexBook, there are graphing calculator activities designed to supple-
ment the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9732.