635.sagews

#simple Runga-Kutta Order 4

var('t','y')
f(t,y) = y
start = 0.0
end = 1.0
solution(t) = float(e)^t
numOfIterations = 2
h = (end-start)/numOfIterations

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

for i in range(numOfIterations):
    s1 = f(t00,y00)
    s2 = f(t00+h/2,y00+h/2*s1)
    s3 = f(t00+h/2,y00+h/2*s2)
    s4 = f(t00+h,y00+h*s3)
    y00 = y00+h/6*(s1+2*s2+2*s3+s4)
    t00=t00+h
    soln.append([t00,y00])
  
    print "%10r %20r %20r"%(t00,y00,solution(t00))

0.500000000000000 1.64843750000000 1.64872127070013 1.00000000000000 2.71734619140625 2.71828182845905