ME 210B
Homework # 4
Due February 18, 2009
1. Consider the RungeKutta method deﬁned by
3

√
3
6

1
4
3

2
√
3
12
3+
√
3
6

3+2
√
3
12
1
4

1
2
1
2
(a) (1 point) Write the formula which corresponds to this Runge
Kutta matrix
(b) (2 points) Using the order conditions from the book, verify that
the method is order 4 (Hint: read Section 4.3 very carefully, in
cluding the examples).
2. (3 points) Write the following in RungeKutta matrix form, and ﬁnd
its order via Taylor expansion:
y
n
+
2
3
=
y
n
+
h
3
[
f
(
y
n
+
2
3
) +
f
(
y
n
)]
y
n
+1
=
y
n
+
h
4
[3
f
(
y
n
+
2
3
) +
f
(
y
n
)]
3. (3 points) It has been argued that displaying absolute stability regions
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This note was uploaded on 07/08/2009 for the course ME 210B taught by Professor Linda during the Spring '09 term at UCSB.
 Spring '09
 Linda

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