How to solve first-order nonlinear differential equation where the solution is coupled with an integral?
2 ビュー (過去 30 日間)
古いコメントを表示
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 件のコメント
採用された回答
David Goodmanson
2019 年 7 月 4 日
編集済み: David Goodmanson
2019 年 7 月 4 日
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 件のコメント
David Goodmanson
2019 年 7 月 8 日
Yes, let me and the website know if there is anything that needs clarification.
その他の回答 (0 件)
参考
カテゴリ
Help Center および File Exchange で Ordinary Differential Equations についてさらに検索
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!