complementary error function (surf plot)

I'm new to MATLAB and i'm trying to plot the following function with surf:

.

Parameter values:

My code so far:

x = linspace(0,10^(-6),20);
t = linspace(0,5,5);
u0 = 10^(-6); 
k = 10^(-9); 

dn = 2.*k.*sqrt(t);
e2 = erf( x.*(dn).^(-1) );
u = u0.*(1 - e2);  
 
surf(x,t,u)
title('Complementary Error function from 0 to 10^(-6)')
xlabel('Distance x')
ylabel('Time t')

I'm trying to get the x between 0 to in increments of and t in increments of .

How do you fix this?

Answer 1

[Star Strider]

Add:

[X,T] = ndgrid(x,t);

and it works:

x = linspace(0,10^(-6),20);
t = linspace(0,5,5);
[X,T] = ndgrid(x,t);
u0 = 10^(-6); 
k = 10^(-9); 

dn = 2.*k.*sqrt(T);
e2 = erf( X.*(dn).^(-1) );
u = u0.*(1 - e2);  
 
surf(X,T,u)
title('Complementary Error function from 0 to 10^(-6)')
xlabel('Distance x')
ylabel('Time t')

although you may want to revise the code a bit.

[Star Strider]

The surf (I used surfc here) plot dedfinitely does show it with the new ranges of ‘x’ and ‘t’:

x = (0:0.01:1)*1E-7;
t = logspace(log10(50), log10(300), 10);
[X,T] = meshgrid(x,t);
u0 = 1E-6; 
k = 1E-9; 

dn = 2.*k.*sqrt(T);
e2 = erf( X./dn );
u = u0.*(1 - e2);  

figure
surfc(X,T,u)
title('Complementary Error function from 0 to 10^(-6)')
xlabel('Distance x')
ylabel('Time t')

I also used logspace to define ‘t’ to provide a more gradual transition, and with this minor modification:

x = (0:0.01:1)*1E-7;
t = logspace(log10(50), log10(300), 10);
[X,T] = meshgrid(x,t);
u0 = 1E-6; 
k = 1E-9; 

dn = 2.*k.*sqrt(T);
e2 = erf( X./dn );
u = u0.*(1 - e2);  

figure
surfc(X,T,u)
set(gca, 'YScale','log')
title('Complementary Error function from 0 to 10^(-6)')
xlabel('Distance x')
ylabel('Time t')

it actually looks better.

[Paul]

Just want to point out that the erfc function can be used directly, and it might be appropriate to use for this problem because u is getting quite small but shouldn't be identically zero. I guess it depends on what, if anything, is to be done with u down stream.

[Stephanie Anderson]

Thank you StarStrider and Paul for your explanations.

[Star Strider]

As always, my pleasure!