I randomly looked at W[2] and it has an extra term with Z[2] (the last term) that is not in the paper. So is it some earlier part that is incorrect that you want to correct? If so please be more specific about where it goes wrong and what you want done.

You should not use the deprecated package linalg. If you just had that for jacobian, the new Jacobian is in VectorCalculus.

It seems like it is a bug. I played around with the first one trying for a workaround but didn't find one. For given numerical values of u__p and x you can numerically estimate the limit by giving a small value to u__m, e.g., -1e-30 with Digits:=50;

@Math-dashti Perhaps this is what you want. It finds the equilibrium points and the Jacobian.

bifur.mw

This version returns the quadratic form in a sum-of-squares form:

Download SumSquares.mw

@Alfred_F The routine I gave here writes a quadratic form in the sum of squares form. I'm not aware of a specific Maple command that does that. But your polynomial is not a quadratic form, so that wouldn't help here.

If by "same line" you mean "in the same execution group (same > prompt) but on the next line" then try shift-enter. If you really mean same line, then don't press enter, just keep typing, separating your commands with semicolons.

Otherwise, please provide a more detailed description of the problem and what you want.

@Suryakanth Did you make those changes?

@salim-barzani I think you want to get rid of z:=0; and later put eval(eqt1, z = 0).

@salim-barzani Sorry, I thought it was wrong to just put z=0 in eq17 by any means, assignment or not. I don't understand what you want to do and have no further comment.

@Suryakanth This time OdeSys and Cond are sets, so to combine them in the dsolve call you need dsolve(OdeSys union Cond,...). The D@@2 need parentheses: (D@@2).

Then you call ContoursWithLabels with argument y=yL..yR but the error message says that it received 0=-0.8..1,5, so you must have set y=0 somewhere.

Look at eq17. A few lines later you assign z:=0. So now eq17 has functions with (x,y,0,t) which presumably don't make sense. This carries through and leads to the D[1](f)(x, y, 0, t) - if you still had the z it would display as an indexed derivative.

This sort of assigning is bad practice in Maple for this reason. Better to use eval(..,z=0) to set z zero only in the things you want and not disrupt all earlier expressions. I'm guessing that you only want z=0 for plotting purposes, so perhaps it should be later? But I'm not sure what is intended here.

@Suryakanth I don't know anything about streamlines. In particular you seem to need psi(x,y) when the odes only gave psi(y).

If you are asking about how to make the contourplot work for the psi_fun you give then note that eval(psi(y), Ans[1]) is a procedure so you need to invoke it at y with eval(psi(y), Ans[1])(y). Also y ranged from -1..1 in that function, not 0..400.

So the following makes the plot work.

pulatile_flow_error.mw

@acer I like it!

@salim-barzani You changed the ode so now there is no w. For the other one {A[0],A[1],A[2],B[0],B[1],B[2],w} takes a very long time and I didn't wait. With 7 equations you have several choices for the 7 variables, so you could try some other options. I don't know how to get a solution.

For the long wave length limit I looked at this before and gave part of the solution, but didn't understand how to get the expression with the theta's. If you have some instructions on how to do that I can take a look.

Do you only have coordinate data or do you also know the identity of the atoms? Are you trying to find the identities from the bond lengths? What class of molecules are you interested in? The variety of bond lengths and hence the tolerance question depends significantly on the class of molecules - what does "heavy-atom molecule" mean?