Runge-Kutta method: Difference between revisions
Added XPL0 example.
Pbartholomew (talk | contribs) |
(Added XPL0 example.) |
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9.0 451.562459 451.562500 -0.000041
10.0 675.999949 676.000000 -0.000051
</pre>
=={{header|XPL0}}==
<syntaxhighlight lang "XPL0">func real Y_(T, Y);
real T, Y;
return T*sqrt(Y);
def DT = 0.1;
real T, Y, Exact, DY1, DY2, DY3, DY4;
[Text(0, " T RK Exact Error^m^j");
T:= 0.; Y:= 1.;
repeat if Mod(T+.001, 1.) < .01 then
[Format(2, 1);
RlOut(0, T);
Format(5, 7);
RlOut(0, Y);
Exact:= sq(T*T+4.)/16.;
RlOut(0, Exact);
RlOut(0, Y-Exact);
CrLf(0);
];
DY1:= DT * Y_(T, Y);
DY2:= DT * Y_(T+DT/2., Y+DY1/2.);
DY3:= DT * Y_(T+DT/2., Y+DY2/2.);
DY4:= DT * Y_(T+DT, Y+DY3);
Y:= Y + (DY1 + 2.*DY2 + 2.*DY3 + DY4) / 6.;
T:= T + DT;
until T > 10.;
]</syntaxhighlight>
{{out}}
<pre>
T RK Exact Error
0.0 1.0000000 1.0000000 0.0000000
1.0 1.5624999 1.5625000 -0.0000001
2.0 3.9999991 4.0000000 -0.0000009
3.0 10.5624971 10.5625000 -0.0000029
4.0 24.9999938 25.0000000 -0.0000062
5.0 52.5624892 52.5625000 -0.0000108
6.0 99.9999834 100.0000000 -0.0000166
7.0 175.5624765 175.5625000 -0.0000235
8.0 288.9999684 289.0000000 -0.0000316
9.0 451.5624593 451.5625000 -0.0000407
10.0 675.9999490 676.0000000 -0.0000510
</pre>
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