How to solve first-order nonlinear differential equation where the solution is coupled with an integral?
2 visualizzazioni (ultimi 30 giorni)
Mostra commenti meno recenti
Califfo
il 3 Lug 2019
Commentato: David Goodmanson
il 8 Lug 2019
I'm trying to solve this nonlinear ODE
- where q is a nonlinear function, solution of ODE;
- represents the velocity and it is equal to: ;
- tis the time:
- the over dot denotes the derivative with respect to time;
- the initial condition is
λ is a degradation parameter of function q and it is equal to:
The integral depends to the solution of ODE.
So I have written this code, but the solution is bad because there isn't degradation of q function
clc
clear
close all
tspan = [0 pi*5];
q0 = 0;
x=@(t)t.*sin(t);
xdot=@(t)t.*cos(t)+sin(t);
lambda = @(t,q) 1+0.01*integral(@(t)q*xdot(t),0,t,'ArrayValued',true);
qdot = @(t,q) xdot(t)*(1-(abs(q)*lambda(t,q)*(0.5+0.5*sign(xdot(t)*q))));
[t,q] = ode45(qdot, tspan, q0);
plot(x(t),q,'LineWidth',2)
0 Commenti
Risposta accettata
David Goodmanson
il 4 Lug 2019
Modificato: David Goodmanson
il 4 Lug 2019
Hi Califfo;
This may be in line with what you want. At least it's changing size It's based on the idea that you know not only qdot, but also lambdadot. That quanity is simply the integrand, .01*q*xdot, and you know that lambda has a starting value of 1. You can make a vector from [q, lambda], which I arbitrarily called z, and then use ode45..
tspan = [0 pi*10];
g0 = 0;
lam0 = 1;
z0 = [g0; lam0];
[t,z] = ode45(@fun, tspan, z0);
x = t.*sin(t);
plot(x,z(:,1))
function zdot = fun(t,z)
xdot = t*cos(t)+sin(t);
q = z(1);
lam = z(2);
qdot = xdot*(1-(abs(q))*(lam/2)*(1+ sign(xdot*q)));
lamdot = 0.01*q*xdot;
zdot = [qdot; lamdot]
end
2 Commenti
David Goodmanson
il 8 Lug 2019
Yes, let me and the website know if there is anything that needs clarification.
Più risposte (0)
Vedere anche
Categorie
Scopri di più su Ordinary Differential Equations in Help Center e File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!