Collect does not do the job

Dear friends,

I have a simple question but after spending an hour I could not figur out how to fix it. So, apologies if this is a simple problem for you. As you see in bellow, I would like to write the following expression in a more compact way:

syms y y0 muY(y) dt

f=(y*diff(muY(y), y, y) - y0*diff(muY(y), y, y) + 2*muY(y)^2 + 2*diff(muY(y), y) + 2*y*muY(y)*diff(muY(y), y) - 2*y0*muY(y)*diff(muY(y), y))/dt;

More clearly, I need to re-write f in terms of (y-y0). As you see, we can do it as bellow (the command collect(f,y-y0) does not work, unfortuantely. Also, the rewrite command is limitted to soem special target functions):

f=((y-y0)*diff(muY(y), y, y) + 2*muY(y)^2 + 2*diff(muY(y), y) + 2*(y-y0)*muY(y)*diff(muY(y), y) )/dt;

which is a much nicer representation for the calculations I need to do.

Any idea?

Thanks in advance!

Babak

Answer 1

[Paul]

Here is one approach showing step-by-step. Many could be combined. Maybe there is a simpler way?

syms y y0 muY(y) dt
f=(y*diff(muY(y), y, y) - y0*diff(muY(y), y, y) + 2*muY(y)^2 + 2*diff(muY(y), y) + 2*y*muY(y)*diff(muY(y), y) - 2*y0*muY(y)*diff(muY(y), y))/dt

f = 

syms D2Y DY
f = subs(f,diff(muY,y,2),D2Y)

f = 

f =subs(f,diff(muY,y),DY)

f = 

[numf,denf] = numden(f)

numf = 

denf = 

dt

syms dely
numf = subs(numf,y,dely + y0)

numf = 

numf = simplify(numf)

numf = 

numf = subs(numf,dely+y0,y)

numf = 

numf = subs(numf,DY,diff(muY))

numf = 

numf = subs(numf,D2Y,diff(muY,y,2))

numf = 

numf = subs(numf,dely,y-y0)

numf = 

f = numf/denf

f = 

[Mohammad Shojaei Arani]

Hi Paul,

That was clever!

Since my intention for such a simplification was to reduce computational time for what I had in mind, I wonder if your recepie is suitable since it also needs quite

a lot of substitutions (given the fact that subs is slow, unfortunately, for very long

algebraic expressions I have. So, this was just a tiny part of my symbolic expressions and I just showed the tip of ice burg!). However, your idea is a good starting point for me to work on and see if I can improve it.

Thanks a lot for your precious time!

Babak