All of the formulas in Table 8-1 in the textbook have a truncation error of O(h), O(h2), or O(h4). Try to derive a four-point, non-centered, finite difference formula for the first derivative of f(x) at x = xi that has a truncation error of O(h3). Moreover, the formula must have the following form: ?′(??) =((??(??−2) + ??(??−1) + ??(??) + ??(??+1))/ℎ)+ ?(ℎ3) In other words, the derivative of f(x) at x = xi must be represented by the combination of the values of f(x) at xi itself, one neighboring grid point to its right, and two grid points to its left, as illustrated in Fig. 1. Show your procedure. Please clearly state the values of A, B, C, and D.

All of the formulas in Table 8-1 in the textbook have a truncation error of O(h), O(h2), or O(h4). Try to derive a four-point, non-centered, finite difference formula for the first derivative of f(x) at x = xi that has a truncation error of O(h3). Moreover, the formula must have the following form: ?′(??) =((??(??−2) + ??(??−1) + ??(??) + ??(??+1))/ℎ)+ ?(ℎ3) In other words, the derivative of f(x) at x = xi must be represented by the combination of the values of f(x) at xi itself, one neighboring grid point to its right, and two grid points to its left, as illustrated in Fig. 1. Show your procedure. Please clearly state the values of A, B, C, and D.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.CR: Chapter 4 Review

Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...

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