633.sagews

#simple example of Euler's Method

var('t','y')
f(t,y) = y
start = 0.0
end = 1.0
solution(t) = float(e)^t
numOfIterations = 10
h = (end-start)/numOfIterations

y00 = 1.0 #initial value
t00 = start;
soln = [[t00,y00]]

for i in range(numOfIterations):
    y00 = y00+h*f(t00,y00)
    t00=t00+h
    soln.append([t00,y00])
    print "%10r %20r %20r"%(t00,y00,solution(t00))

0.100000000000000 1.10000000000000 1.10517091807565 0.200000000000000 1.21000000000000 1.22140275816017 0.300000000000000 1.33100000000000 1.34985880757600 0.400000000000000 1.46410000000000 1.49182469764127 0.500000000000000 1.61051000000000 1.64872127070013 0.600000000000000 1.77156100000000 1.82211880039051 0.700000000000000 1.94871710000000 2.01375270747048 0.800000000000000 2.14358881000000 2.22554092849247 0.900000000000000 2.35794769100000 2.45960311115695 1.00000000000000 2.59374246010000 2.71828182845904

eulers_method?

2.7182818284590451