[5] [General Richardson extrapolation] As mentioned in lecture, Richardson extrapolation is a very general tech- nique that can generate high order approximations from lower order ones. Let N(h) denote some numerical approximation to a derivative (or inte- gral) of some function using step size h, and let T denote the true value of that derivative (or integral). The error in the approximation is E(h) = N(h) — T. Suppose the error ho writton og
[5] [General Richardson extrapolation] As mentioned in lecture, Richardson extrapolation is a very general tech- nique that can generate high order approximations from lower order ones. Let N(h) denote some numerical approximation to a derivative (or inte- gral) of some function using step size h, and let T denote the true value of that derivative (or integral). The error in the approximation is E(h) = N(h) — T. Suppose the error ho writton og
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Richardson extrapol
![[5] [General Richardson extrapolation]
As mentioned in lecture, Richardson extrapolation is a very general tech-
nique that can generate high order approximations from lower order ones.
Let N(h) denote some numerical approximation to a derivative (or inte-
gral) of some function using step size h, and let T denote the true value of
that derivative (or integral).
The error in the approximation is E(h) = N(h) — T. Suppose the error
can be written as
E(h) = c₁h² + c₂h²+1
for some constants c₁ and c2 and some power p.
Determine two constants A and B such that
AE(h/2) + BE(h) = O(h²+¹).
(your answer should depend on p, but not C₁, C2, or h).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fd47556-f3ce-4f39-818d-be563d9523c8%2F46154f0f-c82e-4a9c-817c-3261d012095d%2Fm5l5woh_processed.png&w=3840&q=75)
Transcribed Image Text:[5] [General Richardson extrapolation]
As mentioned in lecture, Richardson extrapolation is a very general tech-
nique that can generate high order approximations from lower order ones.
Let N(h) denote some numerical approximation to a derivative (or inte-
gral) of some function using step size h, and let T denote the true value of
that derivative (or integral).
The error in the approximation is E(h) = N(h) — T. Suppose the error
can be written as
E(h) = c₁h² + c₂h²+1
for some constants c₁ and c2 and some power p.
Determine two constants A and B such that
AE(h/2) + BE(h) = O(h²+¹).
(your answer should depend on p, but not C₁, C2, or h).
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