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Suppose we have a process N(h) to approximate some value M, and we know that N(h) = M + a₁h+ a2h² + a3h³ + a²h¹ +…... Determine a third order accurate approximation to M using N(h), N(h/2), and N(h/3). What order of accuracy can we achieve if a3 = 0? How do we achieve that order of accuracy?

Suppose we have a process N(h) to approximate some value M, and we know that N(h) = M + a₁h+ a2h² + a3h³ + a²h¹ +…... Determine a third order accurate approximation to M using N(h), N(h/2), and N(h/3). What order of accuracy can we achieve if a3 = 0? How do we achieve that order of accuracy?

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
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Numerical Analysis - topic: Finite Differences

Suppose we have a process N(h) to approximate some value M, and we know that N(h) = M + a₁h + a₂h² + a3h³ + a£h ¹ +... Determine a third order accurate approximation to M using N(h), N(h/2), and N(h/3). What order of accuracy can we achieve if a3 =0? How do we achieve that order of accuracy? =
Transcribed Image Text:Suppose we have a process N(h) to approximate some value M, and we know that N(h) = M + a₁h + a₂h² + a3h³ + a£h ¹ +... Determine a third order accurate approximation to M using N(h), N(h/2), and N(h/3). What order of accuracy can we achieve if a3 =0? How do we achieve that order of accuracy? =
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