I attempted to create a phase plot using the Odeplot command in Maple, but the resulting plot isn't as smooth as I'd like. To improve the smoothness, I tried increasing the numpoints parameter to 20,000, but this resulted in the error message: [Length of output exceeds limit of 1000000]. What adjustments should I make to obtain a smoother phase plot without encountering this error?

restart;
r := 1;
b := 1;
c := 0.01;
a := 0.36;
mu := 0.4;
beta := 0.75;

sys := {diff(x(t), t) = r*x(t) - b*x(t)^2 - c*x(t)*y(t) - beta*x(t)*y(t)/(a + x(t)), diff(y(t), t) = -mu*y(t) + beta*x(t)*y(t)/(a + x(t))};
 
ics := {x(0) = 0.2, y(0) = 0.05};

sol := dsolve(sys union ics, {x(t), y(t)}, numeric, range = 0 .. 20000, maxfun = 0, output = listprocedure, abserr = 0.1e-7, relerr = 0.1e-7)

with(DEtools);
DEplot3d(sys, {x(t), y(t)}, t = 0 .. 20000, [[x(0) = 0.2, y(0) = 0.05]], maxfun = 0, numpoints = 35000, thickness = 1, linestyle = solid);
 

with(plots);
phaseplot := odeplot(sol, [x(t), y(t)], 0 .. 20000, numpoints = 10000, color = red, thickness = 2, axes = boxed, gridlines, title = "Phase-space Diagram");

Download extra_steps.mw

Today in class, we presented an exercise based on the paper titled "Analysis of regular and chaotic dynamics in a stochastic eco-epidemiological model" by Bashkirtseva, Ryashko, and Ryazanova (2020). In this exercise, we kept all parameters of the model the same as in the paper, but we varied the parameter β, which represents the rate of infection spread. The goal was to observe how changes in β impact the system's dynamics, particularly focusing on the transition between regular and chaotic behavior.

Download math_model_eco-epidemiology.mw

Hello,

I'm having trouble updating an old Maple package to work with the latest version of Maple. In the package, there are several commands that modify predefined procedures and then rename them (see the example below). I need to save all these new procedures to a text file so I can further modify them and better understand their functionality. How can I achieve this?

d_remset := subs(`class`=`d_class`,`remseta`=`d_remseta`,`premas`=`d_premas`,op(`remset`)):

remset is a procedure previously defined.  

Many thanks.

Obs.: If you have a better idea on how to deal with the procdures, please let me know. 

Dear power users, I was wondering whether it is possible to import a xlsx file in such a way that the first row of the file is imported as column headers of the dataframe in Maple? Thank you in advance for any help given.

Here is another ode solution by Maple, I am not able to get zero from odetest. 

If someone could come up with a trick or method to verify this, that will be great. I tried all sort of assumptions and not able to get zero. Even coulditbe() could not give zero. 

It is a Chini ode and also homogeneous, `class G`.

Solving using either method, odetest do not returns zero.  There are no initial conditions. I am sure the solutions are correct, but odetest need some help or may be this requires different method to verify not using odetest?

Worksheet below.

Download challenge_odetest_sept_1_2024.mw

What is the correct syntax in Maple to do integration of variables on 

So that the new integration variable is y using the mapping    u=y*x^(1/3) so that the result is 

The problems seems is that there is no option to tell Maple what the new integration variable is. So it does not know it should be y or x?

I looked at help and all my tries failed. Below is worksheet and also examples from another software as reference. The other software has argument to tell change of variable what is the new integration variable should be. But in Maple, there is no such option.,  Does this mean in Maple change of integration variables only works when the right hand side of the transformation has only one symbol and not two or more? i.e. this works   u=y, but not u=y*x

Download change_of_variables_integration_august_31_2024.mw

I searched help and see nothing specific to change of variable for integration, so I assumed the above is the command to use. Am I using the wrong command for integration change of variables in Maple?

For reference, I need to duplicate this in Maple:

If there any way to make text  parallel to a line in textplot3d.

display(line([1,2,3],[4,5,-2],linestyle=longdash),
        point([2.5,3.5,0.5]),
        textplot3d([2.5,3.5,0.5,"not aligned"]))

Is one not supposed to make _Z local variable?  If not, then how to insure the global _Z do not have some value assigned to it?

In this example below, I build some integral. I used local _Z for upport limit. But now Maple generate internal error.

If I do not declare _Z as local, and leave it global, then no error is generated.

But if I also declare _Z inside the proc as global _Z, then the error also goes away.

So is one always supposed to use _Z as global? 

The strange thing _Z is protected, so I cant assign to it value from global space. Message says Try declaring `local _Z`; see ?protect for details. but when I do that, I still get an error. 

So is the bottom line here is that one should not declare _Z local to a proc, and just assume it is always global symbol that has no assigned value to it, and that will always be safe to do?  I do not assign value to _Z inside my proc. Just wanted to use it for upper limit, as symbol.

Download using_Z_inside_proc_august_28_2024.mw

For me this result is suspicious. What do you think? 

This ode diff(y(x),x) = f*y(x)^4+g*y(x)+h; is clearly quadrature, since I did not tell Maple that f,g,h depend on x. So this can be solved by just integration. But when asking odeadvisor if it is Chini, it says yes. When asking it what type it is, now it says it is quadrature.

Am I missing something here? I was expecting [NONE] when asking it if it is Chini.

Yes, the ode has the form of Chini, which is   y'=f(x)*y^n + g(x)*y + h(x), where n=4 here. But if f,g,h do not depend on x, then this is now just quadrature. Right? Calling it Chini is little misleading I think.

Download question_on_advisor_august_28_2024.mw

Notice another problem in this solutions. If g=0, then the Chini solution gives divison by zero now, while the quadrature solution still works.

In my Maple 2020, I noticed my program got stuck (overnight so let's say for at least 8 hours) on factorization of relatively small integer, so I tried the command standalone:

ifactor(630743190664091077)

and it just froze. For comparsion I tried other SW and programming libraries and basically all of them had the answer instantly. Also looking at the Maple's methods, if I force pollard or lenstra, it also gets the answer instantly. If my understanding is correct, it gets stuck on the method 'morrbril' which is part of the default mix (I tried also mpqs and it gave FAIL, but at least instantly). 

Is that something that still happens by default in newer versions? Seems to me if it gets stuck on 18 decimal digit integer, maybe it's not the best default method...

Why Maple can not do this basic combining of two terms? What do  I need to do to help Maple do it? Am I not using the correct command?

Download how_to_combine_august_28_2024.mw

For reference, using another software, this is what it gives

SimpleMarsBlyProcedure.mw

Hello Orbital Mechanics and astrodynamics designers of Maple Primes! I am trying to fly to Mars and enter into orbit around it! I know there are a few of you out there that have thought about doing that! Think of all the great mathematicians who have "dabbled" with orbits and astrodynamics! Anyway, here is my problem: I have a simple keplerian model for doing a flyby around Mars and I have a simple model for Reaction Control Thrusters (RCS) to help put the spacecraft into orbit around Mars.  The first thruster burn happens as the spacecraft enters Mars' Sphere Of Influence (SOI) when it is less than 577000 km away and that burn is needed.  I do that with a piecewise continous function with the conditions set up to fire the thrusters.  But in that same piecewise continous function, I have a 2nd thruster firing with the times called out to fire again.  But this time I want to fire the thruster at periapse (P) in order to go into orbit around Mars.  I believe that the Rosenbrock and/or RKF45 are not responding to the 2nd conditions in the piecewise function I have set up for the thruster firing times.  I have to fire the thruster at periapse and I know that time I reach the periapse point.  Also, in my Maple file you will see that I can "cant" the spacecraft to better control the direction of my burns.  

The problem I am encountering seems to be more about the piecewise functions with multiple conditions and expressions.  Please take a look at my Maple file and see if any of you Orbital Mechanics and/or astrodynamicsts familar with Maple can see what I am doing wrong here.  You don't have to be a astrodyamicist per se, just perhaps you have run across this problem of piecewise functions in dsolve with method = rosenbrock or RKF45. 

Thank you. 

Writng the Pde wave function solution in a textbook form ?
golfvergelijking_oplossing_gebruiken_om_integraaluisom_te_halen_voorbeeld.mw

Hi all guys, it is simple equation, I wanna get the expression of w=()^(1/4) which consists zg & fg. I use solve command but fails, could you please help me?

Download solve_an_equation.mw

Hi dear mapleprime users, i have a problem in a change of varibales if the following ode. i want to use "r=R*rs,u(r)=h*u(R*rs)" variable changes in ode, how can i do that, R is a constant. tnx for the help

Download change_of_variables.mw