def solve_equation(p, q, r, x_a, x_b, y_a, y_b, n, method_name, draw_flag, m):
h = (x_b-x_a) / float(n)
xs = map(lambda j: x_a + h*j, range(1, n))
# create matrix
b = map(lambda x: -h*h*r(x), xs)
b[0] += (1.0 + h/2.0 * p(xs[0])) * y_a
b[-1] += (1.0 - h/2.0 * p(xs[-1])) * y_b
a = map(lambda x: -1.0 + h*p(x)/2.0, xs[:-1])
d = map(lambda x: 2 + h*h*q(x), xs)
c = map(lambda x: -1.0 - h*p(x)/2.0, xs[1:])
# solve (thomas)
for k in range(1, n-1):
quot = a[k-1] / d[k-1]
d[k] -= quot * c[k-1]
b[k] -= quot * b[k-1]
x0 = map(lambda x: 0,range(n-1))
x0[n-2] = b[n-2] / d[n-2]
for k in range(n-3, -1, -1):
x0[k] = (b[k] - c[k] * x0[k+1]) / d[k]
xs.insert(0,x_a)
xs.append(x_b)
x0.insert(0,y_a)
x0.append(y_b)
f_y = []
xx = arange(x_a, x_b, 0.1)
for i in xs:
f_y.append(calculate_f_x_2b(i, k, m))
mean_square_error = calculate_mean_square_error(xs,f_y, x0)
max_error = calculate_max_norm(xs, f_y, x0)
mean_format = "{:.4f}"
max_format = "{:.4f}"
if mean_square_error < 0.0001:
mean_format = "{:.3e}"
elif mean_square_error > 100:
mean_format = "{:.0f}"
if max_error < 0.0001:
max_format = "{:.3e}"
elif max_error > 100:
max_format = "{:.0f}"
print(";".join((str(n),mean_format.format(mean_square_error), max_format.format(max_error))))
if draw_flag:
add_to_plot(xs, calculate_f_x_2b(xs, k, m), "given f")
add_to_plot(xs, x0, "Finite difference method")
file_name = method_name + "_"+str(n)
title = method_name + " n = "+str(n)+"\n mean square error = " + mean_format.format(mean_square_error) + "\n max error = " + max_format.format(max_error)
draw_plot(title, file_name)
def create_matrix(k, m, a, b, n, h, f):
a_matrix = zeros(shape=(n+1, 3))
b_matrix = zeros(shape=(n+1, 1))
a_matrix[0] = [0, 2 + h*h*m*m , -1]
b_matrix[0] = 2*m*math.cos(m*a)*h*h + 1
a_matrix[n] = [-1, 2 + h*h*m*m, 0]
b_matrix[n] = 2*m*math.cos(m*b)*h*h + calculate_f_x_2b(b, k, m)
x = [float(a)]
t = a + h
factors = [-1, m*m*h*h + 2, -1]
for i in range(1, n):
t += h
x.append(t)
a_matrix[i] = factors
b_matrix[i] = -h*h*f(t, k, m)
x.append(b)
x.reverse()
return (a_matrix, b_matrix, x)
