How to solve 2nd order ODE inequality ?
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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
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3 comentarios
Respuestas (1)
Tamir Suliman
el 29 de Nov. de 2016
Editada: Tamir Suliman
el 29 de Nov. de 2016
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 comentarios
Tamir Suliman
el 2 de Dic. de 2016
Editada: Tamir Suliman
el 2 de Dic. de 2016
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
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