#### asympt() with multiple variables? (16.2.01)

##### Daniel Krofchick

I am trying to simplify several long expressions using the assumption that some constants in the expression are much larger than others. The expressions are obtained by solving a cubic. Here is the code

where all $$Kij>0$$ and presumably Real (since they represent rate constants). The assumption I want to use to simplify the expression is K12,K21,K34,K43>>K23,K32).

Is there any way to do this in Maple 6? I have been playing with asympt which works well when I want to make this kind of assumption for one variable (in a simpler system derived from a cubic), but the function isn’t deﬁned for multiple variables.

##### Chris Eilbeck (19.2.01)

One way would be to write K23= t*k23, K32 = t*k32, and expand in a Taylor series in t. But the answer is still very messy in this case, even with t=0!

##### Boris Alexeev (20.2.01)

Towards solution:

Is this from chemical kinetics? YES!

chemical reaction

diﬀerential equations

Jacobi matrix

get Jacobi matrix

switch asymptotics on

switch asymptotics oﬀ

get crude solution (one eigenvalue)

get next (and last) approximation (two values)

##### Helmut Kahovec (21.2.01)

Instead of K12,K21,K34,K43 >> K23,K32 I’d like to prefer K23,K32 << K12,K21,K34,K43. Then we may use mtaylor() as shown in the Maple6 session below.

Unfortunately, I could not ﬁnd another way to force Maple to choose the appropriate branch cut:

Finally, let us check the solutions: