이헌식_전산물리_과제13.py

from math import *
import numpy as np
import matplotlib.pyplot as plt

def f(x,y):
    return 1/(x + sqrt(x**2 + 1)) - y/(sqrt(x**2 + 1))

def Runge_Kutta(f,x,t):
    h = t[1] - t[0]
    for i in range(len(x)-1):
        k1 = h*f(t[i],x[i])
        k2 = h*f(t[i]+h/2, x[i]+k1/2)
        x[i+1] = x[i] + k2
    return x, t

t = np.linspace(0,10,1000)
x = np.zeros(len(t), float)

x,t = Runge_Kutta(f,x,t)


plt.plot(t,x, 'r-', label = "coding")
plt.xlabel(r'$x$')
plt.ylabel(r'$y(x)$')
plt.legend()
plt.show()