Calculate derivatives in a non-uniform grid
 

I have a non-uniform 2D grid (non-equal intervals between nodes). [x,y]
I also have the data (U) calculated on this grid.
I want to calculate the derivatives of U with respect to y and then x.

How can I do this? (Specially using MATLAB)

Is it rectangular grid?



You could just use matrix operations ie


dmyfdx = (myf(2:end)-myf(1:end-1)) / (coordx(2:end)-coordx(1:end-1))


where myf is your variable and coordx is the x coordinate in the grid. If this is not sufficiently helpful then please create a small test case demonstrating the data format in a small example. Thanks.

Yes, it is rectangular ,but your solution is only useful for first order - first derivative. How about second order and second derivative?

I think you can view the formulas here


http://web.media.mit.edu/~crtaylor/calculator.html


Vary the number of input points to get the desired order of accuracy.

For example, you have the value f1,f2,f3 at x1,x2,x3. Then you can define a lagrangian second degree polynomial and compute analytically the derivative. More nodes allow you to increase the degree of the polynomial and the accuracy of the derivative.


Have also a look to the textbook of Peric & Ferziger

Thank you ,but this is for uniform grids.