how do i find numerical schemes

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

[William Rose]

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]

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

[Bjorn Gustavsson]

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]

@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]

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

[Ls]

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]

@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]

I tried this way for forward difference but have an error

N=length(t);

ef=1./[t(N+1)-t(N);diff(t)];

D_F4=sparse(1:N,1:N,ef,N,N)-sparse(1:N,[N-1,1:N-1],ef,N,N);

help is highly appreciated.

[Ls]

in this i am trying to create sparse matrix

[William Rose]

@Ls, I am sorry but someone else will have to answer since I have becoe busy.