Need to rectify error in my matlab code given below

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Jasmine
Jasmine 2024-10-1
编辑： Torsten 2024-10-1
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?
  2 个评论
Torsten
Torsten 2024-10-1
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
Jasmine 2024-10-1
I want to get a plot of dn/dt versus t.
Can you please correct my code which will help me solve my problem.

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回答（2 个）

Hitesh
Hitesh 2024-10-1
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))
Torsten
Torsten 2024-10-1
编辑：Torsten 2024-10-1
Ran in:
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)
  3 个评论
显示 1更早的评论
Jasmine
Jasmine 2024-10-1
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
Torsten 2024-10-1
编辑：Torsten 2024-10-1
Ran in:
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

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