Simpson's rule in numerical methods
up vote
1
down vote
favorite
In the following code I have implemented composite Simpson's rule. However I should be getting approximately $291$ but for some reason I am getting something different. I implemented a few other methods to test it and the proper answer was $291$ So how do I fix my code?
from math import pi,cos,sin
def SimpsonMethod(f,a,b,n):
h = (b-a)/n
s = f(a)+f(b)
for i in range(1,n,2):
s+=4*f(a+i*h)
for i in range(2,n-1,2):
s+=2*f(a+h*h)
return s*h/3
print(SimpsonMethod(lambda x: x**2,5,10,100))
giving the output
237.39917687499988
numerical-methods
edited Dec 4 at 0:47
Bernard
117k637109
asked Dec 4 at 0:46
fr14
38318
add a comment |
up vote
1
down vote
favorite
In the following code I have implemented composite Simpson's rule. However I should be getting approximately $291$ but for some reason I am getting something different. I implemented a few other methods to test it and the proper answer was $291$ So how do I fix my code?
from math import pi,cos,sin
def SimpsonMethod(f,a,b,n):
h = (b-a)/n
s = f(a)+f(b)
for i in range(1,n,2):
s+=4*f(a+i*h)
for i in range(2,n-1,2):
s+=2*f(a+h*h)
return s*h/3
print(SimpsonMethod(lambda x: x**2,5,10,100))
giving the output
237.39917687499988
numerical-methods
edited Dec 4 at 0:47
Bernard
117k637109
asked Dec 4 at 0:46
fr14
38318
There are related sites in this group of sites for coding Q's.
– DanielWainfleet
Dec 4 at 2:23
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
In the following code I have implemented composite Simpson's rule. However I should be getting approximately $291$ but for some reason I am getting something different. I implemented a few other methods to test it and the proper answer was $291$ So how do I fix my code?
from math import pi,cos,sin
def SimpsonMethod(f,a,b,n):
h = (b-a)/n
s = f(a)+f(b)
for i in range(1,n,2):
s+=4*f(a+i*h)
for i in range(2,n-1,2):
s+=2*f(a+h*h)
return s*h/3
print(SimpsonMethod(lambda x: x**2,5,10,100))
giving the output
237.39917687499988
numerical-methods
edited Dec 4 at 0:47
Bernard
117k637109
asked Dec 4 at 0:46
fr14
38318
In the following code I have implemented composite Simpson's rule. However I should be getting approximately $291$ but for some reason I am getting something different. I implemented a few other methods to test it and the proper answer was $291$ So how do I fix my code?
from math import pi,cos,sin
def SimpsonMethod(f,a,b,n):
h = (b-a)/n
s = f(a)+f(b)
for i in range(1,n,2):
s+=4*f(a+i*h)
for i in range(2,n-1,2):
s+=2*f(a+h*h)
return s*h/3
print(SimpsonMethod(lambda x: x**2,5,10,100))
giving the output
237.39917687499988
numerical-methods
numerical-methods
edited Dec 4 at 0:47
Bernard
117k637109
asked Dec 4 at 0:46
fr14
38318
edited Dec 4 at 0:47
Bernard
117k637109
asked Dec 4 at 0:46
fr14
38318
edited Dec 4 at 0:47
Bernard
117k637109
edited Dec 4 at 0:47
Bernard
117k637109
edited Dec 4 at 0:47
Bernard
117k637109
117k637109
asked Dec 4 at 0:46
fr14
38318
asked Dec 4 at 0:46
fr14
38318
asked Dec 4 at 0:46
fr14
38318
38318
There are related sites in this group of sites for coding Q's.
– DanielWainfleet
Dec 4 at 2:23
add a comment |
There are related sites in this group of sites for coding Q's.
– DanielWainfleet
Dec 4 at 2:23
There are related sites in this group of sites for coding Q's.
– DanielWainfleet
Dec 4 at 2:23
There are related sites in this group of sites for coding Q's.
– DanielWainfleet
Dec 4 at 2:23
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
Typo in the part of the function that calculates the even nodes, should be s+=2*f(a+i*h), this is after fixing:
from math import pi,cos,sin
def SimpsonMethod(f,a,b,n):
h = (b-a)/n
s = f(a)+f(b)
for i in range(1,n,2):
s+=4*f(a+i*h)
for i in range(2,n-1,2):
s+=2*f(a+i*h)
return s*h/3.
print(SimpsonMethod(lambda x: x**2,5,10,100))
and the result
291.66666666666674
answered Dec 4 at 1:00
caverac
12.6k21027
thanks for the submission! I see where I went wrng
– fr14
Dec 4 at 1:06
1
@fr14 Happy to help
– caverac
Dec 4 at 1:06
I have posted another question using gauss quadrature
– fr14
Dec 4 at 1:47
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Typo in the part of the function that calculates the even nodes, should be s+=2*f(a+i*h), this is after fixing:
from math import pi,cos,sin
def SimpsonMethod(f,a,b,n):
h = (b-a)/n
s = f(a)+f(b)
for i in range(1,n,2):
s+=4*f(a+i*h)
for i in range(2,n-1,2):
s+=2*f(a+i*h)
return s*h/3.
print(SimpsonMethod(lambda x: x**2,5,10,100))
and the result
291.66666666666674
answered Dec 4 at 1:00
caverac
12.6k21027
thanks for the submission! I see where I went wrng
– fr14
Dec 4 at 1:06
1
@fr14 Happy to help
– caverac
Dec 4 at 1:06
I have posted another question using gauss quadrature
– fr14
Dec 4 at 1:47
add a comment |
up vote
1
down vote
accepted
Typo in the part of the function that calculates the even nodes, should be s+=2*f(a+i*h), this is after fixing:
from math import pi,cos,sin
def SimpsonMethod(f,a,b,n):
h = (b-a)/n
s = f(a)+f(b)
for i in range(1,n,2):
s+=4*f(a+i*h)
for i in range(2,n-1,2):
s+=2*f(a+i*h)
return s*h/3.
print(SimpsonMethod(lambda x: x**2,5,10,100))
and the result
291.66666666666674
answered Dec 4 at 1:00
caverac
12.6k21027
thanks for the submission! I see where I went wrng
– fr14
Dec 4 at 1:06
1
@fr14 Happy to help
– caverac
Dec 4 at 1:06
I have posted another question using gauss quadrature
– fr14
Dec 4 at 1:47
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Typo in the part of the function that calculates the even nodes, should be s+=2*f(a+i*h), this is after fixing:
from math import pi,cos,sin
def SimpsonMethod(f,a,b,n):
h = (b-a)/n
s = f(a)+f(b)
for i in range(1,n,2):
s+=4*f(a+i*h)
for i in range(2,n-1,2):
s+=2*f(a+i*h)
return s*h/3.
print(SimpsonMethod(lambda x: x**2,5,10,100))
and the result
291.66666666666674
answered Dec 4 at 1:00
caverac
12.6k21027
Typo in the part of the function that calculates the even nodes, should be s+=2*f(a+i*h), this is after fixing:
from math import pi,cos,sin
def SimpsonMethod(f,a,b,n):
h = (b-a)/n
s = f(a)+f(b)
for i in range(1,n,2):
s+=4*f(a+i*h)
for i in range(2,n-1,2):
s+=2*f(a+i*h)
return s*h/3.
print(SimpsonMethod(lambda x: x**2,5,10,100))
and the result
291.66666666666674
answered Dec 4 at 1:00
caverac
12.6k21027
answered Dec 4 at 1:00
caverac
12.6k21027
answered Dec 4 at 1:00
caverac
12.6k21027
answered Dec 4 at 1:00
caverac
12.6k21027
12.6k21027
thanks for the submission! I see where I went wrng
– fr14
Dec 4 at 1:06
1
@fr14 Happy to help
– caverac
Dec 4 at 1:06
I have posted another question using gauss quadrature
– fr14
Dec 4 at 1:47
add a comment |
thanks for the submission! I see where I went wrng
– fr14
Dec 4 at 1:06
1
@fr14 Happy to help
– caverac
Dec 4 at 1:06
I have posted another question using gauss quadrature
– fr14
Dec 4 at 1:47
thanks for the submission! I see where I went wrng
– fr14
Dec 4 at 1:06
thanks for the submission! I see where I went wrng
– fr14
Dec 4 at 1:06
1
1
@fr14 Happy to help
– caverac
Dec 4 at 1:06
@fr14 Happy to help
– caverac
Dec 4 at 1:06
I have posted another question using gauss quadrature
– fr14
Dec 4 at 1:47
I have posted another question using gauss quadrature
– fr14
Dec 4 at 1:47
add a comment |
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Dec 4 at 2:23