from root_bisection import *
from root_regula_falsi import *
from root_regula_falsi_mod import *
from root_ridder import *
def f(x):
return x**4 - 8*x**3 - 35*x**2 + 450*x - 1001
xl = 5.5 #4.5
xu = 10.0 #6.0
xr = root_bisection(f, xl, xu)
xr = root_regula_falsi(f, xl, xu)
xr = root_regula_falsi_mod(f, xl, xu)
xr = root_ridder(f, xl, xu)
from math import sqrt, tanh
from root_regula_falsi import *
from root_bisection import *
from root_ridder import *
g = 9.81
v = 5.0
t = 2.5
L = 4.0
def f(H):
x = sqrt(2 * g * H)
return v - x * tanh(x / (2 * L) * t)
def calc_v(H):
x = sqrt(2 * g * H)
return x * tanh(x / (2 * L) * t)
Hl = 0.0
Hu = 2.0
Hr = root_bisection(f, Hl, Hu)
print("v = ", calc_v(Hr), " (should be close to ", v, ")")
Hr = root_regula_falsi(f, Hl, Hu)
print("v = ", calc_v(Hr), " (should be close to ", v, ")")
Hr = root_ridder(f, Hl, Hu)
print("v = ", calc_v(Hr), " (should be close to ", v, ")")
from math import exp
from root_regula_falsi import *
from root_bisection import *
from root_ridder import *
g = 9.81
t = 4.0
v = 36.0
m = 82.0
def f(c):
return v - g*m/c*(1 - exp(-c*t/m))
def calc_v(c):
return g*m/c*(1 - exp(-c*t/m))
cl = 3.0
cu = 5.0
cr = root_bisection(f, cl, cu)
print("v = ", calc_v(cr), " (should be close to ", v, ")")
cl = 3.0
cu = 5.0
cr = root_regula_falsi(f, cl, cu)
print("v = ", calc_v(cr), " (should be close to ", v, ")")
cl = 3.0
cu = 5.0
cr = root_ridder(f, cl, cu)
print("v = ", calc_v(cr), " (should be close to ", v, ")")
from root_regula_falsi import *
from root_bisection import *
from root_regula_falsi_mod import *
from root_ridder import *
r1 = 0.5
r2 = 1.0
h = 1.0
ρf = 200.0
ρw = 1000.0
def calc_V_frustum(r1, r2, h):
return pi * h / 3 * (r1**2 + r2**2 + r1 * r2)
# h1/h = (r2-r1)/r
# -> r = (r2-r1)*h/h1
def f(h1):
r = (r2 - r1) * h / h1
Vw = calc_V_frustum(r1 + r, r2, h - h1) # displaced volume of water
Vf = calc_V_frustum(r1, r2, h) # cone volume
return ρw * Vw - ρf * Vf
xr = root_regula_falsi(f, 0.1, 1.0, NiterMax=1000)
xr = root_regula_falsi_mod(f, 0.1, 1.0, NiterMax=1000)
xr = root_bisection(f, 0.01, 1.0, NiterMax=1000)
xr = root_ridder(f, 0.01, 1.0, NiterMax=1000)
from math import exp
from root_regula_falsi import *
from root_bisection import *
from root_ridder import *
g = 9.81
c = 15
t = 10.0
v = 36.0
def f(m):
return v - g*m/c*(1 - exp(-c*t/m))
def calc_v(m):
return g*m/c*(1 - exp(-c*t/m))
ml = 1.0
mu = 100.0
mr = root_bisection(f, ml, mu)
print("v = ", calc_v(mr), " (should be close to ", v, ")")
ml = 1.0
mu = 100.0
mr = root_regula_falsi(f, ml, mu)
print("v = ", calc_v(mr), " (should be close to ", v, ")")
ml = 1.0
mu = 100.0
mr = root_ridder(f, ml, mu)
print("v = ", calc_v(mr), " (should be close to ", v, ")")
from root_bisection import *
from root_regula_falsi import *
from root_ridder import *
Q = 20.0
g = 9.81
def f(y):
B = 3 + y
Ac = 3 * y + y**2 / 2
return 1 - Q * B / (g * Ac**3)
yl = 0.5
yu = 2.5
yr = root_bisection(f, 0.5, 2.5)
yr = root_regula_falsi(f, 0.5, 2.5)
yr = root_ridder(f, 0.5, 2.5)