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2. P, = 3¬P-+, n21 is linearly convergent to the limit p. Generate the first four terms of the sequence using Aitken's A² method with Po = 0.5.

2. P, = 3¬P-+, n21 is linearly convergent to the limit p. Generate the first four terms of the sequence using Aitken's A² method with Po = 0.5.

Advanced Engineering Mathematics
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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numerical methods

2. P, = 3-Pa-1, n21 is linearly convergent to the limit p. Generate the first four terms of the sequence using Aitken's A² method with Po = 0.5.
Transcribed Image Text:2. P, = 3-Pa-1, n21 is linearly convergent to the limit p. Generate the first four terms of the sequence using Aitken's A² method with Po = 0.5.
Expert Solution
Step 1

Aitken's ∆2 Method:- is based on the assumption that the sequence  p^n defined by

 p^n=pn-pn+1-pn2pn+2-2pn+1+pn

converges more rapidly to p than does the original sequence.

Note:- we'll find pn using original sequence.

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