Hello

I need to use the Ritt algorithm to find the characteristic sets of a set of differential equations. In the past, it seems there was a Maple package by D. Wang available through Maple Applications, but this no longer appears to be the case. I managed to download an old set of files from the author’s site, dated February 1996, which is a Maple V3 package. The instructions in the Readme file mention that using the provided Makefile, an m-file containing all the functions will be created, which can then be loaded into Maple. Unfortunately, running make -f Makefile did not create anything, so I am wondering if I could get some assistance on how to convert this package to something compatible with the latest Maple releases.

The source (txt) files are structured as follows:

Example: 

1) Comments
2) Definition of the User functions - something like

 

dcharsets[dcharset] := proc() `charsets/d_charset`(args) end:

dcharsets[dmcharset] := proc() `charsets/d_mcharset`(args) end:

dcharsets[dcs] := proc() `charsets/d_charser`(args) end:

dcharsets[dmcs] := proc() `charsets/d_mcs`(args) end:

dcharsets[dics] := proc() `charsets/d_ics`(args) end:

and

read `charsets.m`:

# set of non-zero remainders of d-polys in ps wrt d-ascending set as
#       user level function
`charsets/d_remset` :=

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

and lots of Maple procedures - Example below

 

`charsets/d_charset` := proc(ps,lst,medset)

....

end:

the source file ends with the following lines.

read dhelp;
save `dcharsets.m`:
quit

Many thanks

Note: Before posting this question here, I tried to contact the author but received no response.

Hello

Here is the ODE

sys := {diff(w(t), t) = y(t)*z(t), diff(x(t), t) = a*w(t), diff(y(t), t) = x(t)*z(t) + w(t), diff(z(t), t) = -x(t)*y(t), w(0) = w0, x(0) = x0, y(0) = y0, z(0) = z0}

with initial parameters a=2, w0 = -0.727367040, x0 = -0.728244724, y0 = -0.237753623 and z0 = 0.014225402.

With these parameters I have no problem to plot the solution.

nsys := subs({a=2,w0 = -0.727367040, x0 = -0.728244724, y0 = -0.237753623, z0 = 0.014225402},sys);

numsol := dsolve(nsys, numeric, method = rkf45);

vars:=[x,y,z,w];

with(plots):

col := [red, magenta, cyan, blue]:
display(
  seq(
    plots:-odeplot(numsol, [t, vars[i](t)], t=0..3, color=col[i], legend=vars[i](t))
    , i=1..numelems(vars)
  )
)

How to use animate (or explore?)  with a slider for each parameter (a,x0,y0,z0,w0)? And if I want to add a tfinal as well for the simulation (in place of 3)? ( I am newbie as far as using plot and related functions in Maple).  

Many thanks. 

Hello

Consider,  as an example,  the following (simple) transcendental equation. 

alpha*((epsilon-1)*x+y-3*x*z-epsilon/3*x^3+b*sin(w)+3)

How to retrieve the coefficients and the terms considering that the unknowns are x,y,z and w?   Something like [x,y,x*z,x^3,sin(w),1] and their coefficients.  

many thanks

Hello

I am trying to understand how to use Maple to solve a PDE.  Below it is a problem (Henon-Heilles system) where the answer is known.  

with(PDEtools);

infolevel[pdsolve]:=3:

declare(Hamil(x,y,u,v));

PDEHamil := u*diff(Hamil(x, y, u, v), x) + v*diff(Hamil(x, y, u, v), y) + (-2*x*y - x)*diff(Hamil(x, y, u, v), u) + (-x^2 + y^2 - y)*diff(Hamil(x, y, u, v), v) = 0;

pdsolve(PDEHamil)

Maple returns no solution, but one solution is:

sH:=1/2*(u^2+v^2)+1/2*(x^2+y^2-2/3*y^3)+x^2*y;

simplify(eval(subs(Hamil(x,y,u,v)=sH,PDEHamil)));
    0=0

What am I missing?

Many thanks.

Hello,

I need to check if Maple can solve a specific PDE. Since I don't know much about the PDEtools package, I wonder if a user familiar with it and experienced in solving PDEs could help me.

with(PDEtools);
declare(u(x,y,z,w));
PDE1:=alpha*(y+b*(w))*diff(u(x,y,z,w),x)+(x+z-b*(w))*diff(u(x,y,z,w),y)-c*y*diff(u(x,y,z,w),z)+d*(y-x)*diff(u(x,y,z,w),w)=0;
Sol1:=pdsolve(PDE1);

Maple returns NULL as the solution. Any ideas on how to obtain a solution, if possible? In other similar PDEs, u(x,y,w,z) has a quadratic form.

Many thanks,