import numpy as np

def khi(X):
    khi = np.zeros_like(X)
    khi[(X >= -1/4) & (X <= 1/4)] = 1
    return khi

def Uinit(X,J):
    Uinit = np.zeros(J)
    Uinit[:] = 256 * ((X[:]-1/4)**2) * ((X[:]+1/4)**2) * khi(X)[:]
    return Uinit

"""def Uinit(X,J):
    Uinit = np.zeros(J)
    Uinit[:] = khi(X)[:]
    return Uinit"""

def schema1(U0,J,alpha):
    U0=np.append(U0[J-2],U0)
    U1=U0[1:J+1] - alpha*(U0[1:J+1]-U0[0:J])
    return U1

def schema2(U0,J,alpha):
    U0=np.append(U0[J-2],U0)
    U0=np.append(U0,U0[1])
    U1=U0[1:J+1]-(alpha/2)*(U0[2:J+2]-U0[0:J])+(0.5*alpha**2)*(U0[2:J+2]-2*U0[1:J+1]+U0[0:J])
    return U1

def schema3(U0,J,alpha):
    U0=np.append(U0[J-2],U0)
    U0=np.append(U0[J-3],U0)
    U0=np.append(U0,U0[1])
    U1=U0[2:J+2]-alpha*(U0[2:J+2]-U0[1:J+1])-((alpha/4)*(1-alpha)*(U0[3:J+3]-U0[2:J+2]-U0[1:J+1]+U0[0:J]))             
    return U1