Annonymouse

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These are questions asked by Annonymouse

I am interested in dynamic systems that changes system equations at a given point in time. So i often want to plot graphs that shows what would happen in the first 500 seconds, then using the point reached after 500 seconds as the starting point show what happens over the next 500 seconds.

For example my equations might innitially

diff(x,t)=x+p*y

diff(y,t)=x/y

and then after 500 seconds switch to 

diff(x,t)=x-p*y

diff(y,t)=x/y

simply estimating where the system is and feeding that into the other equation isn't an option because these equations have lots of parameters which p is representing in the above, and generally i want too use these graphs to illustrate the behaveious of the systems with the given parameters.

So far i use display and DEplot to make these grpahs.

Non dimensionalisation is a vary common task, and I was suprised that I couldn't find a maple tool to automate it . Has anyone developed their own package for it?

I want to automatically do it to the system equations for some Dynamical systems to make some of the other processing I do with them easier.

I was hoping to start with somehting in the form of 

Diff(x[1],t)=f[1](p[1]....p[n],x[1]...x[m])

...

Diff(x[m],t)=f[m](p[1]....p[n],x[1]...x[m])

where each f[i] is some kind of quotient of multivariate polynomials in the variables and parameters:
and end up with something like

Diff(y[1],s)=f[1](q[1]....q[p],y[1]...y[m])

...

Diff(y[m],s)=f[m](q[1]....q[p],y[1]...y[m])

where p<n

I am able to get unlimeted numbers of equations describing my system. These equations are generally relate quotients of multivariate polynomials. Each additional equation I get is generally less than twice the length of the last, and it is not always the case that an equation is independant of the previous equations. Although I can get unlimited numbers of equations describing the system, it is not overdetermined.

I am interested in solving these equations for their variables. There are about 30 cases I am working on, the smallest number of evariables is six, the largest would be twenty.

I want to be able to solve these equations in the minimal time possible. But I don't understand the function solve well enough to do so.

How do I choose the equations to minimise the time taken for the command solve to proccess them?
How does the command solve work?

particularly:

  1. if I process the command solve([Eq1,Eq2,Eq3...Eqn],variables) would the command solve([Eq[1],Eq[2],Eq[3]...Eq[n],Eq[n+1]],variables) take longer if Eq[n+1] is not indipendant of the previous equations? 
  2. Is there a way of checking whether Eq[n+1] is independant of the previous vequations, fast enough for it to be useful to check the equations before they are processed?
  3. Does the ordering of the equations affect the speed of solve?
  4. Is there a way of pre processing the equations before they are put into solve that will save it time? (for example factorising them, simplifying them etc...)

 

 

I am running Maple in a windows virtual machine, on a mac computer.

I have a number of worksheets on its disk

Windows advised me to run its error checking utility (chkdsk)

when I try and open them it gives me a number of options:

maple text

plain text 

and maple input

 

None of these are the same as the original files. What has happened? and how can i fix it?



 I have a system of 4 rational equations involving 6 variables. I want to solve this system for 4 variables. 


Whenver I try to do this I get either an error message about solutions being lost, or maple being unable to allocate enough memory.

The Commands involved are here: 

 

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