Find A, B which make the approximation. So S(x)dæ = Ahƒ(0) + Bhf() as high order as possible. With your choice of A, B, what is the degree of precision, and what is the order of the error (power of h that the global error is proportional to) in this approximation?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. Find A, B which make the approximation.
Sở (z)dx = Ahf(0) + Bhf(4)
as high order as possible. With your choice of A, B, what is the degree
of precision, and what is the order of the error (power of h that the
global error is proportional to) in this approximation?
Aht Bh
At B=1
%3D
f=x
th= 5c" x dc = Bh
12
fox?
dx =Bh
.3
'x'
1
B=?
degree of greeism= 2
Och?)
so
emor
Transcribed Image Text:2. Find A, B which make the approximation. Sở (z)dx = Ahf(0) + Bhf(4) as high order as possible. With your choice of A, B, what is the degree of precision, and what is the order of the error (power of h that the global error is proportional to) in this approximation? Aht Bh At B=1 %3D f=x th= 5c" x dc = Bh 12 fox? dx =Bh .3 'x' 1 B=? degree of greeism= 2 Och?) so emor
Expert Solution
Step 1

Use the following concepts, to determine the solution.

  • The degree of precision is the largest positive integer n, the degree of the polynomial fx=xk, for k=0,1,2,,n, for which the integration formula is exact.
  • The order of accuracy is dependent on the step size h in the numerical method.
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