Need to rectify error in my matlab code given below

syms t

mu=2500*(10^-4); %cm^2*V^-1 * s^-1

R = 0.318;

eta=377;% ohm

N=3.681; %refindex

Pavg=7;%W

Za=50;%ohm

g=100*(10^-6);%m

pi=3.14;

alpha= 8.5*(10^4); %m^-1

taul= 35*(10^-15); %s

tauc= 10*(10^-12); %s

W=100*(10^-6); %m

L=300*(10^-6); % m

Tlt=325*(10^-6); % m

V=25; %V

E=V./g;

vopt=375*(10^12); %Hz

e=1.602*(10^-19);

h=6.626*(10^-34);

I=0.90*(10^8);% i

t=linspace(-0.5*(10^-12),3.0*(10^-12),100);

n(t)=I.*exp(-2).*((1-R)./(sqrt(2.*pi).*h.*vopt)).*taul.*exp((-taul.^2)./(8.*tauc.^2)).*exp(-t./tauc).*(erf(sqrt(2).*t./taul - (sqrt(2).*taul)./(4.*tauc))+1);

tc = 10.*(10.^-12);

n0=10.^18

dt=80.*(10^-12);

G=n0.*exp((-t.*t)/(dt.*dt))

ode = diff(n,t) == (-n./tc) + G;

cond = n(0) == n0;

nSol(t)=dsolve(ode,cond);

It shows difference order N must be a positive integer. Error in third last line. How to solve this error?

[Torsten]

I don't understand what you want to do with your code.

If you define n(t) as a function of t, diff(n,t) == (-n/tx) + G is not a differential equation, but an algebraic relation. Thus using "dsolve" on it makes no sense.

[Jasmine]

I want to get a plot of dn/dt versus t.

Can you please correct my code which will help me solve my problem.

Answer 1

[Hitesh]

Hi Jasmine,

The error you encounter is due to the incorrect use of symbolic differentiation and the definition of “n(t)” as a symbolic function. You can fix this by ensuring that “n(t)” is defined correctly as a symbolic function and that the differentiation is performed on a symbolic expression.

Here are key modifications that are required in your code:

• Declare “n(t)” as a symbolic function using “syms n(t)”.
• Define “n_expr” as a symbolic expression for “n(t)”.
• Use “subs” to evaluate “nSol” over the range “t_vals”.
• Correct the use of “pi” by defining “pi_val” to avoid conflict with MATLAB's built-in “pi”.

syms t n(t) % Declare n as a symbolic function of t 

E = V / g; 

t_vals = linspace(-0.5 * (10^-12), 3.0 * (10^-12), 100); 
 
% Define the expression for n(t) 
n_expr = I * exp(-2) * ((1 - R) / (sqrt(2 * pi_val) * h * vopt)) * taul * ... 
         exp((-taul^2) / (8 * tauc^2)) * exp(-t / tauc) * ... 
         (erf(sqrt(2) * t / taul - (sqrt(2) * taul) / (4 * tauc)) + 1); 
tc = 10 * (10^-12); 
n0 = 10^18; 
dt = 80 * (10^-12); 

% Define G(t) 
G_expr = n0 * exp((-t * t) / (dt * dt)); 

% Define the differential equation 
ode = diff(n, t) == (-n / tc) + G_expr; 

% Evaluate the solution over the specified range
nSol_vals = double(subs(nSol, t, t_vals))

Answer 2

[Torsten]

I want to get a plot of dn/dt versus t.

syms t
mu=2500*(10^-4); %cm^2*V^-1 * s^-1
R = 0.318;
eta=377;% ohm
N=3.681; %refindex
Pavg=7;%W
Za=50;%ohm
g=100*(10^-6);%m
pi=3.14;
alpha= 8.5*(10^4); %m^-1
taul= 35*(10^-15); %s
tauc= 10*(10^-12); %s
W=100*(10^-6); %m
L=300*(10^-6); % m
Tlt=325*(10^-6); % m
V=25; %V
E=V./g;
vopt=375*(10^12); %Hz
e=1.602*(10^-19);
h=6.626*(10^-34);
I=0.90*(10^8);% i
n=I.*exp(-2).*((1-R)./(sqrt(2.*pi).*h.*vopt)).*taul.*exp((-taul.^2)./(8.*tauc.^2)).*exp(-t./tauc).*(erf(sqrt(2).*t./taul - (sqrt(2).*taul)./(4.*tauc))+1);
dn = diff(n,t);
tnum=linspace(-0.5*(10^-12),3.0*(10^-12),100);
dnnum = subs(dn,t,tnum);
plot(tnum,dnnum)

[Jasmine]

Thank you so much

[Jasmine]

I have a query.

My differential equation is:

dn/dt= -(n/tc)+G

how can I get a plot between dn/dt and t?

[Torsten]

syms t n(t)
tc = 10.*(10.^-12);
n0=10.^18;
dt=80.*(10^-12);
G=n0.*exp((-t.*t)/(dt.*dt));
ode = diff(n,t) == (-n./tc) + G;
cond = n(0) == n0;
nSol(t)=dsolve(ode,cond);
dnSol(t) = -nSol(t)/tc + G;
fplot(dnSol,[-0.5*(10^-12),3.0*(10^-12)])
grid on