from math import sqrt

import numpy


#___________________________________________


#x
t0 = 0
tn = 20
#y
x0 = 0
v0 = 0
#equation coefficient
m  = 0.5
p  = 2
k  = 0.5
#metavariables
h  = 0.2
n  = int((tn-t0/h))


t =[1] *n
v =[2] *n
x =[3] *n

v[1]= v0

t = numpy.arange(t0, tn + h, h)
x = [x0]


def F(t,v,x):
 return -(1 /m)*k*x **(p-1)
def solve_system_F():

  for i in range(n):
   k1 = h * F(t[i]        ,x[i]       , v[i]         )
   k2 = h * F(t[i] + h / 2,x[i]+k1 / 2, v[i] + k1 / 2)
   k3 = h * F(t[i] + h / 2,x[i]+k2 / 2, v[i] + k2 / 2)
   k4 = h * F(t[i] + h / 1,x[i]+k3 / 1, v[i] + k3    )

   dv[i] =(k1+2*k2+2*k3+ k4 )*(1/6)

   v[i]= dv[i-1] + v[i-1]
def sovle_system_v0():
    m1 = h*(v[i])
    m2 = h*(v[i] +  k1*(1/2))
    m3 = h*(v[i] +  k2*(1/2))
    m4 = h*(v[i] +  k3)

    dx[i] = (m1 + 2 * m2 + 2 * m3 + m4) * (1 / 6)
    x[i + 1] = x[i] + dx[i]

print(x)
print(t)
print(v)

name = ("P_2_Oscill.txt")
result = open(name, "w")

for f in range(0, n+1):
 result.write(str(t[f]) + ' ' + str(v[f]))
 result.write("\n")
result.close()



#nho define array de viet mang pha tu.
#____________________________________________________

	#f = open('p_2_Oscilattion.txt', "w")
	#line = ""
	#for i in range(n+1):
	#	line = line + str(t[i]) + "\t"
	#	for j in range(eq_num):
	#		line = line + str(y[j][i]) + "\t"
	#	line = line + "\n"
	#f.write(line)


#file = open("p_2O_sci.txt","w")
#for i in a:
 #file1.write(str(i))
#file.close()