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.

Question

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.

BlackTom AI · Accepted Answer

When we talk about discretising space and time for numerical calculations, indices are used to label discrete grid points.
Options like A_{i-1}, A_{i+1}, or A_{i-1/n} reflect values of the parameter A evaluated at specific grid locations relative to the index i.
In this statement, A_{i-1/n} is described as the estimate of A immediately adjacent to location index i, at the current time. The key idea is that the subscript points to a neighboring grid point in space (i.e., not at i itself), with the time level indicated as the current time level (often denoted n or t^n in finite-difference schemes).
If i-1/n is interpreted as a point just to the left of i on the spatial grid, then it indeed corresponds to the adjacent spatial location next to i, evaluated at the current time step. The phrase "immediately adjacent" aligns with the concept of a neighboring node on the discretised grid, rather than a value at i itself or a non-adjacent point.
However, this notation can be ambiguous in isolation: some conventions would write A_{i-1} for the left neighbor and A_{i+1} for the right neighbor, or A_{i-1/n} to denote a point between grid points depending on how the grid and indexing are defined. The statement survives this ambiguity provided one adopts the interpretation that i-1/n designates the adjacent node immediately next to i on the spatial lattice, at the current time step.
In summary, under the common interpretation that the subscript indicates a neighboring spatial location relative to i and that the time index corresponds to the current time level, the description given in the statement correctly identifies A_{i-1/n} as the estimate of A at the adjacent location to i at the current time.

AMME2000 BMET2960 BMET9960 (ND) Week 4 Pre-work

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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