Runge-Kutta method: Difference between revisions
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adding maxima |
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y[t] -> 1/16*(4+t^2)^2 /. t -> Range[10]
->y[{1,2,3,4,5,6,7,8,9,10}]->{25/16, 4, 169/16, 25, 841/16, 100, 2809/16, 289, 7225/16, 676}</lang>
=={{header|Maxima}}==
<lang maxima>'diff(y,x) = x*sqrt(y);
ode2(%, y, x);
ic1(%, x=0, y=1);
factor(solve(%, y)); /* [y=(x^2+4)^2/16] */
rk4(f, x0, y0, x1, n) := block([h, x, y, vx, vy, k1, k2, k3, k4],
h: bfloat((x1 - x0)/(n - 1)),
x: x0,
y: y0,
vx: makelist(0, n + 1),
vy: makelist(0, n + 1),
vx[1]: x0,
vy[1]: y0,
for i from 1 thru n do (
k1: bfloat(h*f(x, y)),
k2: bfloat(h*f(x + h/2, y + k1/2)),
k3: bfloat(h*f(x + h/2, y + k2/2)),
k4: bfloat(h*f(x + h, y + k3)),
vy[i + 1]: y: y + (k1 + 2*k2 + 2*k3 + k4)/6,
vx[i + 1]: x: x + h
),
[vx, vy]
)$
[x, y]: rk4(lambda([x, y], x*sqrt(y)), 0, 1, 10, 101)$
plot2d([discrete, x, y])$
s: map(lambda([x], (x^2 + 4)^2/16), x)$
for i from 1 step 10 thru 101 do print(x[i], " ", y[i], " ", y[i] - s[i]);</lang>
=={{header|Perl 6}}==
{{works with|niecza|2012-04-3}}
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