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1. Use Taylor series to show the order of accuracy (truncation error) in the following approximations to du/dx a) Из+1 — и-1 2Ax b) U¡ – Uj-1 Ax c) Ui+3 – Uj-3 6Ax d) -li+2 + 8ui+1 – 8u;-1 + Uj-2 12Δx Which one gives a better (more accurate) result? What are the trade-offs in using one vs the other?

1. Use Taylor series to show the order of accuracy (truncation error) in the following approximations to du/dx a) Из+1 — и-1 2Ax b) U¡ – Uj-1 Ax c) Ui+3 – Uj-3 6Ax d) -li+2 + 8ui+1 – 8u;-1 + Uj-2 12Δx Which one gives a better (more accurate) result? What are the trade-offs in using one vs the other?

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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1. Use Taylor series to show the order of accuracy (truncation error) in the following approximations to du/dx

1. Use Taylor series to show the order of accuracy (truncation error) in the following approximations to du/dx a) Иi+1 — И-1 2Ax b) и; — и-1 Ax Ui+3 – Uj-3 6Ax d) —и+2 + 8и+1 — 8и-1 + и-2 12Δx Which one gives a better (more accurate) result? What are the trade-offs in using one vs the other?
Transcribed Image Text:1. Use Taylor series to show the order of accuracy (truncation error) in the following approximations to du/dx a) Иi+1 — И-1 2Ax b) и; — и-1 Ax Ui+3 – Uj-3 6Ax d) —и+2 + 8и+1 — 8и-1 + и-2 12Δx Which one gives a better (more accurate) result? What are the trade-offs in using one vs the other?
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