|
=={{header|Python}}==
===using lambda===
<lang Python>def RK4(f):
return lambda t, y, dt: (
lambda dy1: (
lambda dy2: (
lambda dy3: (
lambda dy4: (dy1 + 2*dy2 + 2*dy3 + dy4)/6
)( dt * f( t + dt , y + dy3 ) )
)( dt * f( t + dt/2, y + dy2/2 ) )
)( dt * f( t + dt/2, y + dy1/2 ) )
)( dt * f( t , y ) )
def theory(t): return (t**2 + 4)**2 /16
from math import sqrt
dy = RK4(lambda t, y: t*sqrt(y))
t, y, dt = 0., 1., .1
while t <= 10:
if abs(round(t) - t) < 1e-5:
print("y(%2.1f)\t= %4.6f \t error: %4.6g" % ( t, y, abs(y - theory(t))))
t, y = t + dt, y + dy( t, y, dt )
</lang>
{{Out}}
<pre>y(0.0) = 1.000000 error: 0
y(1.0) = 1.562500 error: 1.45722e-07
y(2.0) = 3.999999 error: 9.19479e-07
y(3.0) = 10.562497 error: 2.90956e-06
y(4.0) = 24.999994 error: 6.23491e-06
y(5.0) = 52.562489 error: 1.08197e-05
y(6.0) = 99.999983 error: 1.65946e-05
y(7.0) = 175.562476 error: 2.35177e-05
y(8.0) = 288.999968 error: 3.15652e-05
y(9.0) = 451.562459 error: 4.07232e-05
y(10.0) = 675.999949 error: 5.09833e-05</pre>
=== Alternate solution ===
<lang python>from math import sqrt
|