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)

1st answer:

Towards solution:

Is this from chemical kinetics? YES!

chemical reaction

differential equations

Jacobi matrix

2nd answer:

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: