题目
题目

AMME2000 BMET2960 BMET9960 (ND) Week 5 Pre-work

单项选择题

The backward difference approximation to the gradient of a function  𝑓 at the point 𝑥 𝑖 , which is uniformly sampled with spacing  Δ 𝑥 is:

选项
A.𝑓 𝑖 − 𝑓 𝑖 − 1 Δ 𝑥
B.𝑓 𝑖 + 1 − 𝑓 𝑖 Δ 𝑥
C.𝑓 𝑖 + 1 − 𝑓 𝑖 − 1 2 Δ 𝑥
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标准答案
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思路分析
To tackle this question, let's compare the given finite-difference formulas for estimating the gradient. Option 1: fi − fi−1 Δx. Interpreting this as (fi − fi−1)/Δx, this is the standard backward difference formula, which uses the ......Login to view full explanation

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类似问题

Consider the following domain, discretized by 6 nodes. The solution at node 1 is 20. The solution at node 2 is 10. The solution at node 3 is 5. Assuming that the distance between nodes is 1, which of the following is the value of the central finite difference approximation of the second derivative of the solution at node 2?  

In the context of discretising space and time for numerical calculations, 𝐴 𝑖 − 1 𝑛 + 1  and  𝐴 𝑖 + 1 𝑛 + 1 refer to estimates of parameter A at the same time, but at spatial locations differing by 2 Δ 𝑥 .

In the context of discretising space and time for numerical calculations,  and  refer to estimates of parameter A at the same time, but at spatial locations differing by .

In the context of discretising space and time for numerical calculations,   𝐴 𝑖 − 1 𝑛 refers to the estimate of parameter A immediately adjacent to location index i, at the current time.

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