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Task14.py
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Task14.py
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import numpy as np
n = 10
a, b = -1, 1
h = (b - a) / n
nodes = np.arange(a, b + h, h)
# u(-1) = u(1) = 0
def p(x):
return 1 / (x - 3)
def q(x):
return 1 + x / 2
def r(x):
return -np.exp(x / 2)
def f(x):
return 2 - x
p_x = p(nodes[1:n])
q_x = q(nodes[1:n])
r_x = r(nodes[1:n])
f_x = f(nodes)
# initialize tridiagonal matrix
A = np.zeros((n + 1, 3))
A[1:n, 0] = (-p_x / np.square(h) - q_x / (2 * h))
A[1:n, 1] = -(2 * p_x / np.square(h) + r_x)
A[1:n, 2] = (-p_x / np.square(h) + q_x / (2 * h))
A[0, 1] = -1 # B_0
A[n, 1] = -1 # B_n
f_x[0] = f_x[n] = 0
print(A)
def solve_tdm(A, F):
s = np.zeros(n + 1)
t = np.zeros(n + 1)
y = np.zeros(n + 1)
a, b, c = A[:, 0], A[:, 1], A[:, 2]
g = F
s[0] = c[0] / b[0]
t[0] = -g[0] / b[0]
for i in range(1, n + 1):
s[i] = c[i] / (b[i] - a[i] * s[i-1])
t[i] = (a[i] * t[i-1] - g[i]) / (b[i] - a[i]*s[i-1])
y[n] = t[n]
for i in range(n-1, -1, -1):
y[i] = s[i] * y[i+1] + t[i]
print(s)
print(t)
return y
y = solve_tdm(A, f_x)
print(y)
# n = 10
# a, b = -1, 1
# h = (b - a) / n
# nodes = np.arange(a - h / 2, b + h / 2 + h, h)
#
# print(nodes)
#
#
# def p(x):
# return (2 - x) / (x + 2)
#
#
# def q(x):
# return x
#
#
# def r(x):
# return (1 - np.sin(x)) * x
#
#
# def f(x):
# return np.square(x)
#
#
# p_x = p(nodes[1:n + 1])
# q_x = q(nodes[1:n + 1])
# r_x = r(nodes[1:n + 1])
# f_x = f(nodes)
#
# # initialize tridiagonal matrix
# A = np.zeros((n + 2, 3))
# A[1:n + 1, 0] = (-p_x / np.square(h) - q_x / (2 * h))
# A[1:n + 1, 1] = -(2 * p_x / np.square(h) + r_x)
# A[1:n + 1, 2] = (-p_x / np.square(h) + q_x / (2 * h))
# A[0, 1] = -1 / 2
# A[0, 2] = 1 / 2
# A[n + 1, 0] = 1 / 2
# A[n + 1, 1] = 1 / 2
#
# f_x[0] = f_x[n + 1] = 0
# print(A)
#
#
# def solve_tdm(A, F):
# s = np.zeros(n + 2)
# t = np.zeros(n + 2)
# y = np.zeros(n + 2)
# a, b, c = A[:, 0], A[:, 1], A[:, 2]
# g = F
# s[0] = c[0] / b[0]
# t[0] = -g[0] / b[0]
# for i in range(1, n + 2):
# s[i] = c[i] / (b[i] - a[i] * s[i - 1])
# t[i] = (a[i] * t[i - 1] - g[i]) / (b[i] - a[i] * s[i - 1])
# y[n + 1] = t[n + 1]
# for i in range(n, -1, -1):
# y[i] = s[i] * y[i + 1] + t[i]
# return y
#
#
# y = solve_tdm(A, f_x)
# print(y)