solve a differential equations system with DSOLVE

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Hello.
I need to solve a differential equation's system in matlab composed by 6 equations: 5 of them are differential and se sixth one is linear without derivatives. All the equations contain both the corresponding unknown variable and one or two other unknown variables that are to be calculated in the other equations. Moreover, in each equation I have coefficients that depend from the unknown quantities.
I tried to write in Matlab (i give an example with only 3 derivatives dTi/dt plus a simple linear equation, and without coefficients):
DTg = ((Tg^2+Tamb^2)*(Tg+Tamb))*(Tamb-Tg)+((Tg^2+Tamb^4)*(Tg+Tamb))*(Tpv-Tg);
DTpv = ((Tg^2+Tamb^2)*(Tg+Tamb))*(Tg-Tpv)+(Tf-Tpv)+(Tamb-Tpv);
DTf = ((Tpv-Tf)-(Tf2-Tf0));
Tf2 = 2*Tf-Tf0;
The unknown variables are Tg,Tpv, Tf and Tf2, which are both in the derivatives and in the second member of the equations.
How can I solve that? I tried using:
dsolve('DTg','DTpv','DTf','Tf2','Tg(0)=Tamb','Tpv(0)=300','Tf(0)=Tf0');
but of course it doesn't work because matlab wants to know tha values of Tg, Tpv, Tf and Tf2 in the second members of the equations.
No idea of how to solve this system.
Thank you to everybody answers!
  1 Comment
Valentina
Valentina on 16 Mar 2012
I tried that:
syms x y z w
S = dsolve('Dx - y*c/e - x^3*y*b/e + x*b*Tamb^3/e - x^4*a/e + x^3*b/e + a/e*Tamb^4 + b/e*Tamb^3 + d/e=0',...
'Dy - z*f/m + y*a*Tamb^3/m + y*f/m + y/(m*g) - Y*i*l/m + x^3*y*a/m + x*a*Tamb^3/m - x^4*a/m + Tamb/(m*g) + h/m - i/m - i*l/m*T_ref=0',...
'Dz + w *n/o + z*f/o - y*f/o + n*Tf0/o=0',...
'w -z*2 +Tf0=0');
Doesn't work.

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Accepted Answer

Kai Gehrs
Kai Gehrs on 19 Mar 2012
Hi Valentina, hi All,
I have tried to solve the example symbolically and I also did not find a way. When entering
dsolve('DTg=((Tg^2+Tamb^2)*(Tg+Tamb))*(Tamb-Tg)+((Tg^2+Tamb^4)*(Tg+Tamb))*(Tpv-Tg)',...
'DTpv=((Tg^2+Tamb^2)*(Tg+Tamb))*(Tg-Tpv)+(Tf-Tpv)+(Tamb-Tpv)',...
'DTf=((Tpv-Tf)-(Tf2-Tf0))',...
'Tf2=2*Tf-Tf0','Tg(0)=Tamb','Tpv(0)=300','Tf(0)=Tf0');
in MATLAB I get the information that the internal system solver cannot handle this kind of problem.
You probably should be looking for a numerical solution. Since the last equation does not contain derivatives, it may be worth trying a numerical solver which can handle "differential algebraic equations". There are solvers in MATLAB which can handle these kinds of equations. Just search the help for "differential algebraic equations" or DAE (the short form).
Best regards,
-- Kai

More Answers (1)

Sean de Wolski
Sean de Wolski on 16 Mar 2012
Did you define those variables as syms?
syms Tg Tpv Tf Tf2
first.
  6 Comments
arnold ing
arnold ing on 4 Sep 2017
Edited: arnold ing on 4 Sep 2017
Hi Its the same for me..its not about the script name

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