Problem 2 Given the data set (Xg, Yk): Xo = 1; Xx = Xx-1 + 0.2 for k = 1 and 2; Y* =sin(2x,) a) Write down the 2nd order Lagrange polynomial constructed from the above data. Show the final result in the compact form: ax? + bx + c, where a,b, and c are to be determined.
Problem 2 Given the data set (Xg, Yk): Xo = 1; Xx = Xx-1 + 0.2 for k = 1 and 2; Y* =sin(2x,) a) Write down the 2nd order Lagrange polynomial constructed from the above data. Show the final result in the compact form: ax? + bx + c, where a,b, and c are to be determined.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Problem 2
Given the data set (Xg, Yk); Xo = 1;
Xg = Xg-1+ 0.2 for k = 1 and 2;
Yk =sin(2xx)
a) Write down the 2nd order Lagrange polynomial constructed from the above data. Show the final result in the
compact form: ax? + bx + c, where a, b, and c are to be determined.
b) Plot the obtained polynomial and the original function on the same graph over an interval [1, 1.4]. Use 0.01
increment while plotting the polynomial and original function.
c) Evaluate the error when the generated polynomial is evaluated at x = 1.3?
d) Compare the error obtained in part e with the error bound.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feffc0def-cbbe-433e-b1d5-a4a12f49f24b%2Fc691cbbb-a8c4-4f0c-975f-0c26ed35241f%2F3ngq7z_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 2
Given the data set (Xg, Yk); Xo = 1;
Xg = Xg-1+ 0.2 for k = 1 and 2;
Yk =sin(2xx)
a) Write down the 2nd order Lagrange polynomial constructed from the above data. Show the final result in the
compact form: ax? + bx + c, where a, b, and c are to be determined.
b) Plot the obtained polynomial and the original function on the same graph over an interval [1, 1.4]. Use 0.01
increment while plotting the polynomial and original function.
c) Evaluate the error when the generated polynomial is evaluated at x = 1.3?
d) Compare the error obtained in part e with the error bound.
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 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
