3. Write a PYTHON function called midpoint quad.py with signature def midpoint quad (func, a, b, N) # quad = midpoint quad ( func, a, b, N) # comments return quad where func indicates the name of a function, a and b are the lower and upper limits of integration, and N is the number of points, not the number of intervals. Test your midpointquad routine by computing f 2xdx = 1. Even if you use only one interval (i.e. N = 2) you should get the exact answer because the midpoint rule integrates linear functions exactly. Use your midpoint routine to estimate the integral of the Runge function, f(x) = 1/(1+x2), over the interval [-5, 5]. The exact answer is 2 arctan (5). Fill in the following table, using scientific notation for the error values so you can see the pattern. Midpoint Result Error N h 11 1.0 101 0.1 1001 0.01 10001 0.001 Estimate the order of accuracy (an integer power of h) by examining the behaviour of the error when h is divided by 10. (In previous problems, we have estimated such orders by repeatedly increasing h. Here, we increase the number of points. The idea is the same.)
3. Write a PYTHON function called midpoint quad.py with signature def midpoint quad (func, a, b, N) # quad = midpoint quad ( func, a, b, N) # comments return quad where func indicates the name of a function, a and b are the lower and upper limits of integration, and N is the number of points, not the number of intervals. Test your midpointquad routine by computing f 2xdx = 1. Even if you use only one interval (i.e. N = 2) you should get the exact answer because the midpoint rule integrates linear functions exactly. Use your midpoint routine to estimate the integral of the Runge function, f(x) = 1/(1+x2), over the interval [-5, 5]. The exact answer is 2 arctan (5). Fill in the following table, using scientific notation for the error values so you can see the pattern. Midpoint Result Error N h 11 1.0 101 0.1 1001 0.01 10001 0.001 Estimate the order of accuracy (an integer power of h) by examining the behaviour of the error when h is divided by 10. (In previous problems, we have estimated such orders by repeatedly increasing h. Here, we increase the number of points. The idea is the same.)
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
100%
![3.
Write a PYTHON function called midpoint quad.py with signature
def midpoint quad (func, a, b, N)
#quad = midpoint quad ( func, a, b, N)
# comments
return quad
where func indicates the name of a function, a and b are the lower and upper limits of
integration, and N is the number of points, not the number of intervals. Test your midpointquad
routine by computing f2rdx = 1. Even if you use only one interval (i.e. N = 2) you should
get the exact answer because the midpoint rule integrates linear functions exactly. Use your
midpoint routine to estimate the integral of the Runge function, f(x) = 1/(1+x2), over the
interval [-5, 5]. The exact answer is 2 arctan (5). Fill in the following table, using scientific
notation for the error values so you can see the pattern.
Midpoint Result Error
N
h
11
1.0
101
0.1
1001
0.01
10001 0.001
Estimate the order of accuracy (an integer power of h) by examining the behaviour of the error
when h is divided by 10. (In previous problems, we have estimated such orders by repeatedly
increasing h. Here, we increase the number of points. The idea is the same.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F01b4eff1-1c92-4d86-9563-264f29556131%2Fd242f8c9-4e2f-4a01-b28f-537663203c5b%2F0ymb1v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.
Write a PYTHON function called midpoint quad.py with signature
def midpoint quad (func, a, b, N)
#quad = midpoint quad ( func, a, b, N)
# comments
return quad
where func indicates the name of a function, a and b are the lower and upper limits of
integration, and N is the number of points, not the number of intervals. Test your midpointquad
routine by computing f2rdx = 1. Even if you use only one interval (i.e. N = 2) you should
get the exact answer because the midpoint rule integrates linear functions exactly. Use your
midpoint routine to estimate the integral of the Runge function, f(x) = 1/(1+x2), over the
interval [-5, 5]. The exact answer is 2 arctan (5). Fill in the following table, using scientific
notation for the error values so you can see the pattern.
Midpoint Result Error
N
h
11
1.0
101
0.1
1001
0.01
10001 0.001
Estimate the order of accuracy (an integer power of h) by examining the behaviour of the error
when h is divided by 10. (In previous problems, we have estimated such orders by repeatedly
increasing h. Here, we increase the number of points. The idea is the same.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
Hi please show the actual coding of the question in python program.
Solution
by Bartleby ExpertKnowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Recommended textbooks for you
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education