Metode Numerik 2 - Universitas Indonesia
Metode Numerik 2 - Universitas Indonesia
Metode Numerik 2 - Universitas Indonesia
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Contoh penyelesaian dengan metode Runge-Kutta orde 4:<br />
( ) ( )<br />
2<br />
0<br />
3<br />
1<br />
2<br />
1<br />
0<br />
2<br />
0<br />
2<br />
1<br />
0<br />
1<br />
0<br />
0<br />
3<br />
2<br />
1<br />
0<br />
6<br />
1<br />
0<br />
0<br />
3<br />
2<br />
0<br />
0<br />
3<br />
2<br />
1<br />
2<br />
1<br />
0<br />
2<br />
1<br />
0<br />
2<br />
1<br />
0<br />
2<br />
1<br />
0<br />
2<br />
1<br />
0<br />
1<br />
0<br />
0<br />
0<br />
0<br />
3<br />
2<br />
1<br />
0<br />
6<br />
1<br />
0<br />
0<br />
hf<br />
u<br />
u<br />
hf<br />
u<br />
u<br />
hf<br />
u<br />
u<br />
y'<br />
u<br />
u<br />
2u<br />
2u<br />
u<br />
h<br />
y<br />
h)<br />
y(x<br />
y)<br />
u(x,<br />
y'<br />
)<br />
u<br />
,<br />
hu<br />
y<br />
h,<br />
f(x<br />
f<br />
)<br />
u<br />
,<br />
hu<br />
y<br />
h,<br />
f(x<br />
f<br />
)<br />
u<br />
,<br />
hu<br />
y<br />
h,<br />
f(x<br />
f<br />
)<br />
u<br />
,<br />
y<br />
,<br />
f(x<br />
f<br />
f<br />
2f<br />
2f<br />
f<br />
h<br />
u<br />
h)<br />
u(x<br />
u)<br />
y,<br />
f(x,<br />
u'<br />
+<br />
=<br />
+<br />
=<br />
+<br />
=<br />
=<br />
+<br />
+<br />
+<br />
+<br />
=<br />
+<br />
=<br />
+<br />
+<br />
=<br />
+<br />
+<br />
=<br />
+<br />
+<br />
=<br />
=<br />
+<br />
+<br />
+<br />
+<br />
=<br />
+<br />
=<br />
0<br />
0 u<br />
,<br />
y 1<br />
u 2<br />
f<br />
2<br />
u 3<br />
u h)<br />
u(x<br />
h),<br />
y(x<br />
,<br />
f 0<br />
0<br />
3<br />
+<br />
+<br />
0<br />
0<br />
0<br />
0<br />
0<br />
0<br />
y<br />
h)<br />
y(x<br />
,<br />
u<br />
h)<br />
u(x<br />
,<br />
x<br />
h<br />
x →<br />
+<br />
→<br />
+<br />
→<br />
+<br />
Alur perhitungan:<br />
1<br />
f<br />
0<br />
f<br />
121