Needs derivative w.r.t. ' y ' & then graph w.r.t ' t '

y=0:0.01:5; 
 P2=5;            %%%   t=1;
U=exp(y*sqrt(P2)).*(1-erf(y./(2.*sqrt(t))+ sqrt(P2.*t)));
S= - diff(U,y);            %%Needs derivative w.r.t.  ' y '  & then its value at y=0
F= - diff(U,1);  
%%NOW  need to graph w.r.t  ' t '
t=0:0.01:5;
 plot(t,F)
  xlabel(' t');
  ylabel('F');

While running the code the following error occurs:

The second argument must be a variable or a nonnegative integer specifying the number of differentiations.

Error in

S= - diff(U,y)

And for F= - diff(U,1)

F=[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] is coming which is of no interest.

[gonzalo Mier]

Can you edit your question to put your code in code format?

Like this

[MINATI]

@gonzalo Mier

Actually I don't know how to do that

Answer 1

[gonzalo Mier]

diff is a function of the symbolic package, so when you try to derivate U, you are derivating a constant, and by a constant, so F is a 0. To do what you want, you should do it in symbolic and then replace your variable, like:

syms y t
P2=5;           
U=exp(y*sqrt(P2)).*(1-erf(y./(2.*sqrt(t))+ sqrt(P2.*t)));
S= - diff(U,y); 

v_t=0.01:0.01:5;
F = subs(S,y,0);
plot(v_t,vpa(subs(F,t,v_t)))
xlabel(' t');
ylabel('F');

[MINATI]

@gonzalo Mier

The following ERROR occurs :

Error using symengine

Division by zero.

Error in sym/subs>mupadsubs (line 140)

G = mupadmex('symobj::fullsubs',F.s,X2,Y2);

Error in sym/subs (line 125)

G = mupadsubs(F,X,Y);

Error in (line 80)

plot(t,subs(F,t,v_t))

[MINATI]

BUT by changing v_t=1:0.01:5;, ERROR is as:

Error using plot

Data must be numeric, datetime, duration or an array convertible to double.

Error in (line 80)

plot(t,subs(F,t,v_t))

[gonzalo Mier]

Because you have a singularity in t=0. Just change the code at the end by:

v_t=0.01:0.01:5;
plot(v_t,vpa(subs(F,t,v_t)))

And please, use the tool to input code when you write code in the forum.

[gonzalo Mier]

I change the code in the answer to make it work

[MINATI]

@ gonzalo Mier

Sorry for accepting the answer late

We had a very bad CYCLONE, So we had no electricity and no internet for last days

Thats why I accepted late

[gonzalo Mier]

Oh sorry, I hope you and your family are ok.

Once a week I just see the answers I have answer that week and clean the ones that were accepted or comment the ones that seems solved. Sorry if it was too soon.

Thank you for accepting my answer and my best wishes for you.

[MINATI]

@gonzalo Mier

oh Thanks