Python中使用Runge-kutta四阶的ODE系统
我正在编写一个python程序,在给定两个初始条件的情况下求解2x2系统的一阶微分方程。我的代码:Python中使用Runge-kutta四阶的ODE系统,python,ode,runge-kutta,Python,Ode,Runge Kutta,我正在编写一个python程序,在给定两个初始条件的情况下求解2x2系统的一阶微分方程。我的代码: from math import * import numpy as np np.set_printoptions(precision=6) ## control numpy's decimal output :) form1 = raw_input('Enter the 1st function of u & v only >> ') form2 = raw_input(
from math import *
import numpy as np
np.set_printoptions(precision=6) ## control numpy's decimal output :)
form1 = raw_input('Enter the 1st function of u & v only >> ')
form2 = raw_input('Enter the 2nd function of u & v only >> ')
start = input("Enter the lower limit of the interval >> ")
stop = input("Enter the upper limit of the interval >> ")
h = input("Using step size? ")
N = int(np.round((stop - start)/h, decimals = 4)) ##calculate the number of times to iterate
## np.round fixes a python bug returning 2.99999997 instead of
## 3 which reduced the number of times iterated by -1
k = np.zeros((2, 4))
u = np.zeros((N +1,)) ## fill our u's first with N+1 0's
v = np.zeros((N +1,)) ## fill our v's first with N+1 0's
u[0] = input("Give me an initial value for u'>> ")
v[0] = input("Give me the second initial value for v' >> ")
t = np.arange(start, stop + h, h)
def f1(t, u, v):
return eval(form1)
def f2(t, u, v):
return eval(form2)
##for u now
def trialu():
for j in range(0, N):
k[0, 0] = h * f1(t[j], u[j], v[j])
k[1, 0] = h * f2(t[j], u[j], v[j])
k[0, 1] = h * f1(t[j] + h/2, u[j] + 0.5*k[0, 0], v[j] + 0.5*k[1, 0])
k[1, 1] = h * f2(t[j] + h/2, u[j] + 0.5*k[0, 0], v[j] + 0.5*k[1, 0])
k[0, 2] = h * f1(t[j] + h/2, u[j] + 0.5*k[0, 1], v[j] + 0.5*k[1, 1])
k[1, 2] = h * f2(t[j] + h/2, u[j] + 0.5*k[0, 1], v[j] + 0.5*k[1, 1])
k[0, 3] = h * f1(t[j], u[j] + k[0, 2], v[j] + k[1, 2])
k[1, 3] = h * f2(t[j], u[j] + k[0, 2], v[j] + k[1, 2])
u[j+1] = u[j] + (k[0, 0] + 2*k[0, 1] + 2*k[0, 2] + k[0, 3])/6
v[j+1] = v[j] + (k[1, 0] + 2*k[1, 1] + 2*k[1, 2] + k[1, 3])/6
return u
我知道我可以返回(u,v)
,但我想以不同的方式打印“u~”,u
,也可以v
在另一行,但我似乎只需要重复trialu来返回v,有更好的方法吗?不重复def trialu()?我还想打印j=1,2。。。分开?例如,从
[0,0.4]
使用h=0.1
和u[0]=0
和v=0.5的步长求解u'=-3*u+2*v
和v'=3*u-4*v
,我不确定你在问什么,也许这是有用的:
# example u and v
u = [1.003, 1.002, 1.001]
v = [0, 0, 0]
for i, (uapprox, vapprox) in enumerate(zip(u, v)):
print "on iteration", i, "u ~", uapprox, "and v ~", vapprox
输出:
on iteration 0 u ~ 1.003 and v ~ 0
on iteration 1 u ~ 1.002 and v ~ 0
on iteration 2 u ~ 1.001 and v ~ 0
好的,我试试看,稍后再回复。