242.sagews

#
# Euler's method
#

from pylab import *

# time step
h = 0.05

# initial condition
x0 = 2.0
y0 = 4.0

# final point
xn = 2.5

# function (DE)
def fn(x, y):
	return 0.1 * sqrt(y) + 0.4 * x * x;

# algorithm
y = y0
print "xn   yn"
for x in arange(x0,xn+(h/2),h):
	print "%.2lf" % x, "%.4lf" % y
	y = y + h * fn(x, y)

xn yn 2.00 4.0000 2.05 4.0900 2.10 4.1842 2.15 4.2826 2.20 4.3854 2.25 4.4927 2.30 4.6045 2.35 4.7210 2.40 4.8423 2.45 4.9686 2.50 5.0997