non-uniform symmetric grid in 1D

I am trying to make a non-uniform symmetric grid in 1D (dense grid close to the boundaries), is there any simple command?

Answer 1

[Bruno Luong]

The chebychev nodes cross my mind

leftbnd=-10

leftbnd = -10

rightbnd = 10;
n = 30

n = 30

chebychevgrid=@(leftbnd,rightbnd,n)leftbnd+((rightbnd-leftbnd)/2)*(cos(linspace(pi,0,n))+1)

chebychevgrid = function_handle with value:
    @(leftbnd,rightbnd,n)leftbnd+((rightbnd-leftbnd)/2)*(cos(linspace(pi,0,n))+1)

a = chebychevgrid(leftbnd,rightbnd,n)

a = 1×30

-10.0000 -9.9414 -9.7662 -9.4765 -9.0758 -8.5686 -7.9609 -7.2600 -6.4739 -5.6119 -4.6841 -3.7014 -2.6753 -1.6178 -0.5414 0.5414 1.6178 2.6753 3.7014 4.6841 5.6119 6.4739 7.2600 7.9609 8.5686 9.0758 9.4765 9.7662 9.9414 10.0000

plot(a, ones(size(a)),'-o')

[abolfazl mahmoodpoor]

Thanks Bruno for your kind answer.

I also found this, by changing sigma it is possible to control mesh density close to the boundaries.

N = 50;

d = 1;

sigma = d/30;

x50 = d/2;

x = d./(1+exp(-(linspace(0,d,N)-x50)/sigma));

plot(x,0,'bo')

grid on

Answer 2

[Walter Roberson]

No, there is no simple command for it.

If you have the first half, say a row vector B, then you can build the rest as

[B, ENDVALUE-fliplr(B)]

except, that is, for the case where the last B value is exactly half-way through, in which case you do not want to duplicate that value...

You can create your own simple functions for this, but Mathworks does not provide any simple command for it.

[abolfazl mahmoodpoor]

Walter thanks for your kind answer,

I think I didnot asked my question correctly,

My question is following: We know that x = linspace(0,1,N) created a uniform mesh from 0 to 1 with N-1 interval in a way that \deltax = (1-0)/(N-1). So \deltax is constant everywhere, I need to have small \deltax close to the 0 and 1, but the total number of N should be the same, and when move from 0 to 0.5 or from 1 to the 0.5 \deltax should increse gardually.

I hope I could explaine it clear.