How to solve 2nd order ODE inequality ?

Question

Firas Mourad 2016-11-28

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/314367-how-to-solve-2nd-order-ode-inequality

编辑： Tamir Suliman 2016-12-2

Hello to all,

I am trying to numerically solve a 2nd order ODE inequality of the form : y"(x) + y'(x)*a(x) + y(x)*b(x) <= 0 ( a(x) and b(x) are spatially varying parameters). Also, my solution y(x) must be > 0 for all x.

It is possible to solve a similar problem in Matlab ( y"(x) + y'(x)*a(x) + y(x)*b(x) = 0 ) using ode solvers, however, I am uncapable of enforcing the above constraints (ODE<=0 and y(x)>0).

Are toolboxes like Yalmip useful in solving such problems?

Thanks in advance

Firas

3 个评论
显示 1更早的评论隐藏 1更早的评论

Firas Mourad 2016-11-29

I was just wondering if such a problem can be solved using a toolbox like Yalmip. If not, then I welcome other suggestions :)

Firas Mourad 2016-11-29

Just an update. I got a reply from a Yalmip forum : such problems cannot be sloved using Yalmip.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Tamir Suliman 2016-11-29

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/314367-how-to-solve-2nd-order-ode-inequality#answer_245105

编辑：Tamir Suliman 2016-11-29

在 MATLAB Online 中打开

lets assume that we have the equations:

y''+a*y'+b*y<=0 a , b are f(x) where x>0

let y(x)=Y1 and dy(x)/dx = Y2

dY1/dx= Y2 dY2/dx= -a*Y2-b*Y1

lets assume a =3 b =4 then the program code would be similar to

a=3;b=4;
syms y(x)
[V] = odeToVectorField(diff(y, 2) == -a*diff(y) -b* y);
M = matlabFunction(V,'vars', {'x','Y'})
sol = ode45(M,[0 20],[2 0]);
fplot(@(x)deval(sol,x,1), [0, 20])