How to solve 2nd order ODE inequality ?

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Firas Mourad
Firas Mourad 2016-11-28
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
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Firas Mourad
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
Firas Mourad 2016-11-29
Just an update. I got a reply from a Yalmip forum : such problems cannot be sloved using Yalmip.

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回答（1 个）

Tamir Suliman
Tamir Suliman 2016-11-29
编辑：Tamir Suliman 2016-11-29
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])
if statement would be sufficient to add the constraints
  2 个评论
Firas Mourad
Firas Mourad 2016-11-29
Thank you Tamir for your reply.
Could you please elaborate more on how the if statement will be used?
Tamir Suliman
Tamir Suliman 2016-12-2
编辑：Tamir Suliman 2016-12-2
if sol > 0 then code please do some thing for me here
else if sol < 0 then code please do some thing for me else code
end
https://www.mathworks.com/help/matlab/ref/if.html

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