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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?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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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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