I have created a code to solve three coupled ODE but unable to plot its nature on the graph as one of the curve is imaginary .

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Yogesh
Yogesh 2024-1-3
评论： Yogesh 2024-1-8
Ran in:
clc
clear all
alpha=3.55*10^-3;
sigma=3.7292*10^11;
eta=rand;
TB=3.59*10^8;
delta_t=50*10^-12;
n=1.45;
c=3*10^8;
Q=141.3227*10^-4;
syms t p(t) AL(t) AS(t)
% --- move to here ---
real_part=randn();
imag_part=randn();
complex=exp(-(real_part+1i*imag_part))^2;
f=sqrt((n*Q)/((delta_t)^2)*c)*complex; % <-- this parameter must be defined before ODE
r=sqrt((n*Q)/(c*TB))*complex;
% --- move to here ---
Eq1=diff(AL)==1i*sigma*p(t)*AS(t);
Eq2=diff(AS)==1i*sigma*conj(p(t))*AL(t);
Eq3=(alpha/TB)*diff(p,2)+(alpha-1i)*diff(p)-((1i*TB)/2)*p(t)==eta*AL(t)*conj(AS(t))-1i*f;
[VF,subs]=odeToVectorField(Eq1,Eq2,Eq3);
disp(VF)
disp(subs)
% ftotal=matlabFunction(VF);
ftotal = matlabFunction(VF, 'vars', {'t', 'Y'});
tspan = [0 1].*10^-6;
ic = [0 0 r 0]; % <-- 4 states requires 4 initial values (check the order)
[t,Y] = ode45(ftotal, tspan, ic);
plot(t, Y(:, 1), 'LineWidth', 2, 'DisplayName', 'AS');
hold on;
plot(t, Y(:, 2), 'LineWidth', 2, 'DisplayName', 'AL');
plot(t, Y(:, 3), 'LineWidth', 2, 'DisplayName', 'p');
Warning: Imaginary parts of complex X and/or Y arguments ignored.
xlabel('Time');
ylabel('Solution');
title('Solution of the Coupled ODE System');
grid on;
The plot is not showing its display name and one of the curve is imaginary. I dont know how to plot all three at the same plane.

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采纳的回答

Sam Chak
Sam Chak 2024-1-3
Ran in:
Hi @Yogesh
You can plot the real part and the imaginary part separately to verify if this meets your requirements.
alpha=3.55*10^-3;
sigma=3.7292*10^11;
eta=rand;
TB=3.59*10^8;
delta_t=50*10^-12;
n=1.45;
c=3*10^8;
Q=141.3227*10^-4;
syms t p(t) AL(t) AS(t)
% --- move to here ---
real_part=randn();
imag_part=randn();
complex=exp(-(real_part+1i*imag_part))^2;
f=sqrt((n*Q)/((delta_t)^2)*c)*complex; % <-- this parameter must be defined before ODE
r=sqrt((n*Q)/(c*TB))*complex;
% --- move to here ---
Eq1=diff(AL)==1i*sigma*p(t)*AS(t);
Eq2=diff(AS)==1i*sigma*conj(p(t))*AL(t);
Eq3=(alpha/TB)*diff(p,2)+(alpha-1i)*diff(p)-((1i*TB)/2)*p(t)==eta*AL(t)*conj(AS(t))-1i*f;
[VF,subs]=odeToVectorField(Eq1,Eq2,Eq3);
disp(VF)
disp(subs)
ftotal = matlabFunction(VF, 'vars', {'t', 'Y'});
tspan = [0 1].*10^-6;
ic = [0 0 r 0]; % <-- 4 states requires 4 initial values (check the order)
[t,Y] = ode45(ftotal, tspan, ic);
subplot(221)
plot(t, Y(:, 1), 'LineWidth', 2, 'DisplayName', 'AS'), grid on, title('AS')
subplot(223)
plot(t, Y(:, 2), 'LineWidth', 2, 'DisplayName', 'AL'), grid on, title('AL')
subplot(222)
plot(t, real(Y(:, 3)), 'LineWidth', 2, 'DisplayName', 'p'), grid on, title('real(p)')
subplot(224)
plot(t, imag(Y(:, 3)), 'LineWidth', 2, 'DisplayName', 'p'), grid on, title('imag(p)')

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