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how do i find numerical schemes

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Ls 2021-9-29

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评论： William Rose 2021-9-30

How do I calculate forward ,backward and central differences of 50 datas using spdiags command?

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William Rose 2021-9-29

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spdiags extracts the diagnoals from a matrix. There is no direct way to use it to compute differences. Forward, backward, and central differences are normally calculated on a vector. If you have a 50x50 tridiagonal matrix and you wish to compute differences of elements along the diagnal, then please specify the direction in which you want to compute the differences: vertical, horizontal, or perpendicular to the diagonal.

Ls 2021-9-29

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compute the difference in vertical to the diagonal. or by using the comand sparse.

Bjorn Gustavsson 2021-9-29

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What is the spatial relation between the points where you have your "datas" at? Equally spaced along 1-D in space? Randomly distributed in 3-D space? On a 5-by-10 regular 2-D grid?

William Rose 2021-9-29

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在 MATLAB Online 中打开

Ran in:

@Ls,

You said you want vertical differences along the diagonal.

N=5; %aray size NxN
A=magic(N)
A = 5×5
    17    24     1     8    15
    23     5     7    14    16
     4     6    13    20    22
    10    12    19    21     3
    11    18    25     2     9
B=spdiags(A,[-1:1]); %3 columns of B are 3 diagonals of A
diffF=B(:,1)-B(:,2); %vertical forward differences
diffB=B(:,2)-B(:,3); %vertical backward differences
diffC=(B(:,1)-B(:,3))/2; %vertical central differences
disp([diffF,diffB,diffC]); %display results
    6.0000   17.0000   11.5000
    1.0000  -19.0000   -9.0000
    6.0000    6.0000    6.0000
  -19.0000    1.0000   -9.0000
   -9.0000    6.0000   -1.5000

spdiags() inserts zeros for the missing elements of the off-diagonals. Do disp(B) to see this. Good luck!

William Rose 2021-9-29

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@Ls, in the example I posted, note that the central difference (column 3) is always the mean of hte forward and backward difference.

Ls 2021-9-29

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Hello William, I have the data for time, xposition and y position, I have to create a matrix M using command sparse. And i have 50 data in each column not evenly distributed.

William Rose 2021-9-29

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@Ls, It woudl help if you would post the vectors t, x, y ad attachments or as included code. I do not understand what matrix M is supposed to contain. I do not understand how or why you must use command sparse to create M.

Is it your goal to compute dx/dt and dy/dt by forward, backward, and central differences? If that is your goal, you do not need M and u do not need to use sparse().

Ls 2021-9-30