0
1
2
0 1 2
0
1
2
0 1 2
0
1
2
3
0 0.5 1 1.5 2
Euler (h=0.5) Euler (h=0.25) Midpoint
Analytical RK4
0
2
4
6
0 0.2 0.4 0.6 0.8 1
yanal yEuler yHeun yRalston yRK4
©
0
1
2
3
4
5
0 1 2 3
Heun Ralston Midpoint Heun (iter) Exact
y = 0.01777x – 26.80753
R² = 0.99763
7.8
8
8.2
8.4
8.6
8.8
1940 1960 1980 2000
0
2000
4000
6000
8000
10000
1950 1970 1990 2010 2030 2050
pdata panal p-rk4
0
1
2
3
4
00.5
y z
©
-4
-3
-2
-1
0
1
2
3
4
0 2 4 6 8 10
y (h = 0.1)
z (h = 0.1)
y (h = 0.2)
z (h = 0.2)
-5
-4
-3
-2
-1
0
1
2
3
4
0 1 2 3 4
yEuler
yanal
-5
-4
-3
-2
-1
0
1
2
3
4
0 1 2 3 4
yRK4
yanal
