3744.sagews

import numpy as np
def f(t,y):
    res=[y[1],-(y[0]^2)]
    return(np.array(res))

def RK4(a,b,N,ya):
    y=np.empty([2,N+1])  #tableau 2 lignes N+1 colonnes
    h=(b-a)/N
    y[:,0]=ya
    for i in range(N):
        t=a+i*h
        tdemi=t+h/2
        r1=f(t,y[:,i])
        r2=f(tdemi,y[:,i]+(h/2)*r1)
        r3=f(tdemi,y[:,i]+(h/2)*r2)
        r4=f(t,y[:,i]+h*r3)
        y[:,i+1]=y[:,i]+(h/6)*(r1+2*r2+2*r3+r4)
    return (y)

RK4(0,5,10,1)

array([[ 1.00000000e+00, 1.33447266e+00, 1.24812557e+00, 7.90350203e-01, 1.68766077e-01, -4.76809912e-01, -1.19828700e+00, -2.32649094e+00, -5.04840935e+00, -1.65036736e+01, -1.91557328e+02], [ 1.00000000e+00, 2.79373169e-01, -6.01953019e-01, -1.15220442e+00, -1.28485955e+00, -1.31399740e+00, -1.67595853e+00, -3.18259805e+00, -9.45245958e+00, -5.73215667e+01, -2.86171751e+03]])

def Adams(a,b,N,ya):
    y=np.empty([2,N+1])
    h=(b-a)/N
    y[:,0]=ya
    rk4=RK4(a,a+2*h,2,ya)
    y[:,0:3]=rk4
    for i in range(2,N):
        t=a+i*h
        y[:,i+1]=y[:,i]+(h/24)*(9*f(t,y[:,i+1])+19*f(t,y[:,i])-5*f(t,y[:,i-1])+f(t,y[:,i-2]))
    return(y)

Adams(0,5,50,[1])

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_137.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("bT1BZGFtcygwLDUsNTAsWzFdKQpsaXN0X3Bsb3QobGlzdChtKSk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmp_k4xKz/___code___.py", line 4, in <module> exec compile(u'list_plot(list(m))' + '\n', '', 'single') File "", line 1, in <module> File "/sagenb/sage_install/sage-4.7.2/local/lib/python2.6/site-packages/sage/misc/decorators.py", line 534, in wrapper return func(*args, **options) File "/sagenb/sage_install/sage-4.7.2/local/lib/python2.6/site-packages/sage/plot/plot.py", line 3656, in list_plot P = point(data, **kwargs) File "/sagenb/sage_install/sage-4.7.2/local/lib/python2.6/site-packages/sage/plot/point.py", line 312, in point return point3d(points, **kwds) File "/sagenb/sage_install/sage-4.7.2/local/lib/python2.6/site-packages/sage/plot/plot3d/shapes2.py", line 1022, in point3d A = sum([Point(z, size, **kwds) for z in v]) File "/sagenb/sage_install/sage-4.7.2/local/lib/python2.6/site-packages/sage/plot/plot3d/shapes2.py", line 680, in __init__ self.loc = (float(center[0]), float(center[1]), float(center[2])) TypeError: only length-1 arrays can be converted to Python scalars