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Simple Substituting and Rearranging

Hi there.

In a scientific paper I have the following equation

q=aq^3+b [eq1]

eq1 is approximated with q=a^-0.5 + delta [eq2]

delta=-b/2

Where does this approximation come from and why is delta=-b/2?

Thank you very much.
(edited 10 years ago)
Reply 1
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Caccioppoli
OP
I have updated the first message, since there is some progress.
(edited 10 years ago)
Original post by Caccioppoli
I have updated the first message, since there is some progress.


Do you have a link to the paper?
Reply 3
Avatar for Caccioppoli
Caccioppoli
OP
I haven't a link for the paper which is
"Application of the Higuchi model for drug release from dispersed
matrices to particles of general shape" by M. Regina Brophy and P.B. Deasy , 1987

I've found the solution !! :biggrin:

we have two equations, basically:

aq3−q+b=0aq^3-q+b=0 and q=a−0.5+δq=a^{-0.5}+\delta with a small δ

Writing those two equations in a system, we have that the δ that satisfy both equations is a δ that satisfy this 3rd order equation:

aδ3+3a−0.5δ2+2δ+b=0a\delta^3+3a^{-0.5}\delta^2+2\delta+b=0

ignoring third order and second order terms in δ we have simply

2δ+b=02\delta+b=0 so the result δ=−b/2\delta=-b/2

:biggrin:
(edited 10 years ago)
Original post by Caccioppoli

I've found the solution !! :biggrin:


Thanks for posting it.

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