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Torsten
Posts:
1,717
Registered:
11/8/10


Re: A differential inside another differential  DAES
Posted:
Mar 8, 2013 2:35 AM


"Elsis" wrote in message <khaghp$q69$1@newscl01ah.mathworks.com>... > Hello > > I have a set of DAES, but I have one differential inside another something like this: > > Dx(1)=x(2)x(1) > 0=x(2)K*x(1) >>> an algebraic equation > Dx(3)=K*Dx(1)+K*x(3) > > is it possible to solve a system like this on Matlab or I should require to do something extra to solve it? > > thanks! have a nice day! > > Elsa
Three ways to rewrite your DAE system:
Either you define the mass matrix for the system above as M=[1 0 0; 0 0 0; K 0 1] and the righthand side vector as f=[x(2)x(1);x(2)K*x(1);K*x(3)]
or, since Dx1 = x(2)x(1), you can insert this expression directly into the third equation to get Dx(1)=x(2)x(1) 0=x(2)K*x(1) >>> an algebraic equation Dx(3)=K*(x(2)x(1))+K*x(3)=K*(x(2)x(1)+x(3)) and thus M=[1 0 0; 0 0 0; 0 0 1] f=[x(2)x(1);x(2)K*x(1);K*(x(2)x(1)+x(3))] or you solve for x(2) from the algebraic equation and insert in the other two: from the algebraic equation you get x(2)=K*x(1) and thus Dx(1) = x(2)x(1) = K*x(1)x(1)=(K1)*x(1) Dx(3) = K*Dx(1)+K*x(3)=K*(K1)*x(1)+K*x(3)=K*((K1)*x(1)+x(3))
Best wishes Torsten.



