"(x) = Af(xi-1) + Bf(x,) + Cf(x\»1) + Df(x\»z) + Ef(x{+x) , 04n In other words, the second derivative of fx) at x = x, must be represented by the combination of the values of fx) at x, itself, one grid point to its left, and the neighboring three grid points to its right, as illustrated in Fig. 2. Show your procedure. Please clearly state the values of A, B, C, D, and E. h f"(x,) +3
"(x) = Af(xi-1) + Bf(x,) + Cf(x\»1) + Df(x\»z) + Ef(x{+x) , 04n In other words, the second derivative of fx) at x = x, must be represented by the combination of the values of fx) at x, itself, one grid point to its left, and the neighboring three grid points to its right, as illustrated in Fig. 2. Show your procedure. Please clearly state the values of A, B, C, D, and E. h f"(x,) +3
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
Derive a five-point, non-centered, finite difference formula for the second derivative of f(x) at x = xi
that has a truncation error of O(h3). Moreover, the formula must have the following form:
?′′(??) =((??(??−1) + ??(??) + ??(??+1) + ??(??+2) + ??(??+3))/ℎ2) + ?(ℎ3) .
In other words, the second derivative of f(x) at x = xi must be represented by the combination of the
values of f(x) at xi itself, one grid point to its left, and the neighboring three grid points to its right, as
illustrated in Fig. 2. Show your procedure. Please clearly state the values of A, B, C, D, and E.
Transcribed Image Text:c"(x) = Af(x-1) + Bf (x;) + Cf(xi+1) + Df(xi+2) + Ef (xi+3)
h?
+ O(h³).
In other words, the second derivative of f(x) at x = x, must be represented by the combination of the
values of f(x) at x, itself, one grid point to its left, and the neighboring three grid points to its right, as
illustrated in Fig. 2. Show your procedure. Please clearly state the values of A, B, C, D, and E.
f "(x,)
i+1
+2
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
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,
