10/6/2010
Math Modeling 2 (Xin Li)
1
Runge
Runge-Kutta Method
Kutta Method
Math Modeling II
2010
Euler
Euler Method
Method
Euler’s method can be viewed as:
First estimate the derivative
Then, update value
(
)
,
n
n
1
n
n
n
n
y
h
y
y
y
t
f
y
′
+
=
=
′
+
Note:
1. We are using only one value of
f
in estimating
the derivative.
2. Runge-Kutta methods are based on the idea that
using more values of
f
(at two, three, or four
points) may lead to improvements.
Runge
Runge-Kutta Methods
Kutta Methods
Runge-Kutta methods are very popular because they
have higher order of convergence.
The idea is based on using more values of
f
to get better
The idea is based on using more values of
to get better
estimate of the updated value.
They are single-step methods, as the Euler methods.

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