problem with a differential algebraic equation system

Hello, i face problem trying to solve the following differential algebraic equation system:


d(x1)=f1(x1,t)
d(x2)=f2(x2,t)
d(x3)=f3(x3,t)
d(x4)=f4(x4,x5,t)
d(x5)=f5(x4,x5,x6,t,z)
d(x6)=f6(x5,x6,t)
g(x1,x2,x3,t)=0 =>x1(t)+x2(t)+x3(t)=C(constant value) (specifically this is the algebraic function g analytically)
h(x1,x2,x3,x4,x5,t,z)=0 (algebraic function h is more complicated, it includes log function also between the unknown variables)


If you could give me a method to solve it , i would be gratefull.

Till now i'm using numerical analysis to solve it (using ode23 function from matlab), but i do not know how to solve the differential equations in parallel with the algebraic ones.

Thank you in advance

any help please ?

Any differential equation could be written in that way. If there were a general way to solve that system, there would be a general way to solve any differential equation- and there isn't!

Maybe if you just used the algebraic equations to eliminate a couple of the independent variables? Then you'd just have DE's, and you could pass that off to ode23.

I'm giving more info about the variables and the structure of the problem.

K1*(d(x1)/dt)=K2*K3-K4*x1(t)+K5
K1*(d(x2)/dt)=K2*K6-K4*x2(t)-0.5*K5
K1*(d(x3)/dt)=K2*K6-K4*x3(t)

K1*(d(x4)/dt)=K2*K7-K4*x4(t)+K8*(x5(t)-x4(t))
K9*(d(x5)/dt)=K10*(x4(t)-x5(t))+K11*(x6(t)-x5(t))+K12*(K13-x5(t))+Q*K14
K15*(d(x6)/dt)=K16*(K17-x6(t))+K18*(x5(t)-x6(t))

g(x1,x2,x3,t)=0 =>x1(t)+x2(t)+x3(t)=C(constant value)
C=(0.5*K5)/(K4-K2)

Q=K18-K19*[K20+K21*x5(t)*ln(K22*(x2(t)*x4(t))^(0.5))/(x1(t)*x4(t))-K23*x4(t)
-K24+K25*x4(t)*ln(K26/x2(t))]

All Ki (i=1-26) variables are constant and independent.

This is the extended for of the problem. I'm definitelly sure that i didn'd do any mistake at writing that. This is the problem i have to solve.

If someone has any inspiration on that , i would be grateful!

I still stand by Post #4. Do some careful algebra, and eliminate the algebraic equations. You can do that, I think. What's left will be only ODE's; that you can hand over to ode23 in MATLAB.