Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Prove that converting the Higher-Order derivatives to the finite difference formula would be: f(x;) – 2f (x¡-1) + f(xi-2) (Ax)2 1) f"(x;) = "Backward Method" f(xi+2) – 2f(xi+1) + f(x;) 2) f"(xi) = "Forward Method" (Ax)2 f(xi+3) – 3f(xi+2)+ 3f(x;+1) – f(x;) (Ax)3 3) f'(x) = "Forward Method"

Prove that converting the Higher-Order derivatives to the finite difference formula would be: f(x;) – 2f (x¡-1) + f(xi-2) (Ax)2 1) f"(x;) = "Backward Method" f(xi+2) – 2f(xi+1) + f(x;) 2) f"(xi) = "Forward Method" (Ax)2 f(xi+3) – 3f(xi+2)+ 3f(x;+1) – f(x;) (Ax)3 3) f'(x) = "Forward Method"

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Prove that converting the Higher-Order derivatives to the finite difference formula would be: f(x) – 2f(xi-1) + f(x¡-2) (Ax)2 1) f"(x;) = "Backward Method" f(xi+2) – 2f(x;+1) + f(x¡) (Ax)2 2) f"(xi) = "Forward Method" f (xi+3) – 3f(xi+2) + 3f(xi+1) – f(x;) (Ax)3 3) f"'(x;) = "Forward Method"
Transcribed Image Text:Prove that converting the Higher-Order derivatives to the finite difference formula would be: f(x) – 2f(xi-1) + f(x¡-2) (Ax)2 1) f"(x;) = "Backward Method" f(xi+2) – 2f(x;+1) + f(x¡) (Ax)2 2) f"(xi) = "Forward Method" f (xi+3) – 3f(xi+2) + 3f(xi+1) – f(x;) (Ax)3 3) f"'(x;) = "Forward Method"
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Power Series
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 Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS