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Dear Friends

I am trying to find determining system for variable coefficient KdV equation, this system is required to find relevant point symmetries for said equation. Following is set of command that I used to perform task:

This last cammand gives me determining system for PDE1.

Following is direct procedure to find determining system:

This last command give large expression from which determining system is obtained by equating coefficient to zero which does not matches with determining system obtained with first procedure.

What could be the possible error?

I have also attached relevant Maple18 file for analysis.


Dear all,

I am trying to solve the following partial differential equation (transport or advection equation) with given initial and boundary conditions:

restart: with(PDEtools):
sys := [v*diff(u(x,t), x) + diff(u(x,t), t) = 0, u(x,0) = exp(-x), u(0,t) = sin(t)];

But it does not work. The solution is (or should be): 

u(x, t) = exp(t*v-x)+Heaviside(t-x/v)*(sin(t-x/v)-exp(t*v-x))

I think the reason is that the interval for t (in [0, inf)) and x (in [0, 1]) is not specified. On the other hand, this works:

restart: with(PDEtools):
sys := [diff(u(x, t), t) = diff(u(x, t), x, x), u(0, t) = 0, u(1, t) = 0, u(x,0) = f(x)];
sol := pdsolve(sys);

How can I solve a PDE like the transport equation with given initial AND boundary conditions?

Thanks a lot

I am doing some lengthy computation using the externally developed (and published in academic journals) package 'Janet' to compute the compatibility conditions of an overdetermined set of linear PDEs.

At some point in the process (for a set of equations rather, but not SO, complicated) the procedure gives the error

in (PDEtools/NumerDenom) too many level of recursion


I have contacted the developer of the packages and he told me that he never directly calls PDEtools functions, so he deems that that call is made by some more standard maple command (such as simplify).

I could not find any documentation of NumerDenom function, to try and understand what might be the problem (my set of equations has some extremely 'bad' fractions, but I hope this is not that naive)

How does NumerDenom works, and where is it called by 'standard' maple command?

Thank you all.


     I have a question regarding pdsolve, or Solve from the PDEtools package. I have a set of equations relating partial derivatives, and I'd like to isolate certain terms without explicitly known the functions. I can do this for a single equation, but not multiple ones. I'm curious if Maple can currently handle a system of eqns like these easily, since I will be increasing the number of eqns in the future. Here's the code 





H(x, y, t)*`will now be displayed as`*H


eq1:= H[tt](x,y,t) = H[xx](x,y,t) + H[yy](x,y,t);

H[tt](x, y, t) = H[xx](x, y, t)+H[yy](x, y, t)


eq2 := diff(H[tt](x,y,t), t) = diff(H[tx](x,y,t), x) + diff(H[ty](x,y,t), y);

diff(H[tt](x, y, t), t) = diff(H[tx](x, y, t), x)+diff(H[ty](x, y, t), y)


eq3 := diff(H[tx](x,y,t), t) = diff(H[xx](x,y,t), x) + diff(H[xy](x,y,t), y);

diff(H[tx](x, y, t), t) = diff(H[xx](x, y, t), x)+diff(H[xy](x, y, t), y)


eq4 :=diff(H[ty](x,y,t), t) = diff(H[xy](x,y,t), x) + diff(H[yy](x,y,t), y);

diff(H[ty](x, y, t), t) = diff(H[xy](x, y, t), x)+diff(H[yy](x, y, t), y)


PDEtools:-Solve(eq3, H[xy]);

H[xy](x, y, t) = Int(diff(H[tx](x, y, t), t)-(diff(H[xx](x, y, t), x)), y)+_F1(x, t)


PDEtools:-Solve({eq1, eq2, eq3, eq4}, H[xy]);

Error, (in pdsolve/sys) the input system cannot contain equations in the arbitrary parameters alone; found equation depending only on {H[tt](x,y,t), H[xx](x,y,t), H[yy](x,y,t)}: H[tt](x,y,t)-H[xx](x,y,t)-H[yy](x,y,t)






I'm taking my first steps with maple and pdsolve, trying to run the example in the maplesoft support page:

which reads

> restart; with(PDEtools);
> U := diff_table(u(x, t));

and I get a solution that is different from the web page, and when i run

Im using maple 13. Any tips about what's wrong?



Dear Maple users


I have a question about applying pdsolve MAPLE for solving two dimensional heat equations:

My codes have been provided but it shows to me this error:

Error, (in pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent variables, got {t, x, y}

If kindly is possible, please help me in this case.


With kind regards,

Emran Tohidi.


> restart;
> with(plots);
print(??); # input placeholder
> with(PDEtools);
print(??); # input placeholder
> declare(u(x, y, t));
print(`output redirected...`); # input placeholder
                    u(x, y, t) will now be displayed as u
> S := 1/100; tR := 0 .. 1; xR := 0 .. 1; yR := 0 .. 1; NF := 30; NP := 100;
print(??); # input placeholder
> N := 3; L1 := [red, blue, green]; L2 := [0, 1/2, 1]; Ops := spacestep = S, timestep = S;
print(??); # input placeholder
> Op1 := frames = NF, numpoints = NP;
print(??); # input placeholder
> PDE1 := diff(u(x, y, t), t)-(diff(u(x, y, t), `$`(x, 2)))-(diff(u(x, y, t), `$`(y, 2))) = 0;
print(??); # input placeholder
> IC := {u(x, y, 0) = exp(x+y)}; BC := {u(0, y, t) = exp(2*t+y), u(1, y, t) = exp(2*t+y+1), u(x, 0, t) = exp(2*t+x), u(x, 1, t) = exp(2*t+x+1)};
print(??); # input placeholder
> Sol := pdsolve(PDE1, `union`(IC, BC), numeric, u(x, t), Ops);
Error, (in pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent variables, got {t, x, y}

I have a set of partial differential equations and want to find its conserved currents using PDE pakage. 

I define second order partial differential equations as q1,q2,q3,q4 and a set of them: PDE3:={q1,q2,q3,q4} and use the command J[alpha] := ConservedCurrents(PDE3) to calculate its conserved currents but I encounter this error which made me crazy!

Error, (in PDEtools:-DeterminingPDE) invalid input: PartialDerivatives expects value for keyword parameter maxdifforder to be of type nonnegint, but received -1

my equations are like

((1/2)*(diff(R(theta, psi), theta))*(diff(f(theta, psi), theta))+(3/8)*(diff(R(theta, psi), theta))^2+(1/8)*(diff(f(theta, psi), theta))^2+(1/4)*(diff(f(theta, psi), theta, theta))+(1/4)*(diff(R(theta, psi), theta, theta)))*exp(f(theta, psi))+diff(R(theta, psi), psi, psi)-(1/2)*(diff(R(theta, psi), psi))*(diff(f(theta, psi), psi))+(1/2)*(diff(chi(theta, psi), psi))^2 = 0

I don't know what's wrong, can you help me?

Looking at the code of PDEtools:-declare, one sees that it does some brief initializing and then passes the job off to `PDEtools/declare`. I'd like to view this latter procedure, but I can't find it. It is not at the top level, nor is it an export or local of module PDEtools. So where is it?

Hey everybody I am trying to get maple to do some partial differention for me. 



I have PDEtools on but, it doesnt return an expression correctly. It's I think the problem is because Ψ is a function of (x,y) and f is a function of η and η is a function of x and y . U and ν are constants. vand vy are the x and y velocites. 


What I would like the program to return when I write 

is something along the lines of 


could someone give me a hand on this. I would really apperciate it. 


Best Regards, 


I tried using maple to solve the below system of Partial differential equations but itzz not jst coming out... any assistance will be appreciated (post the maple codes if used)

sys2 := -(diff(u(y, t), y, y)) + S*(diff(u(y, t), y)) + diff(u(y, t), t) + M.u(y,t) + (u(y,t)/k)-theta(y,t) = 0,
 -(diff(theta(y, t), y, y))/Pr + diff(theta(y, t), t) + S*(diff(theta(y, t), y)) = 0

The variables are... u(y,t) and theta(y,t)

The initial conditions are;


I have found numerous ways of plotting PDEs, but I am trying to ask Maple to calculate the simple analytical solution of one.

Now, Maple is very happy to solve the following with one initial condition:


pde := diff(u(z, t), t)+c*(diff(u(z, t), z)) = A;
IBC := (u(z, 0) = f(z));



However, when we take, 
IBC := (u(z, 0) = f(z), D[1](u)(0, t) = 0, D[1](u)(-h, t) = 0);

what am i doing wrong???

> restart;
> with(PDEtools);
> a := 3;
> U := u(r, t);
> wave := a^2*(diff(U, r$2))+(diff(U, r))/r) = diff(U,t$2));
> ics := u(1, t) = 0;
> bcs := diff(U, t) = piecewise(0<= r <b,-2, b<= r<1,0), u(r, 0) = 0;
> s := pdsolve(wave, {bcs, ics});

Error, (in pdsolve/sys) too many arguments; some or all of the following are wrong: [{u(r, t)}, {u(1, t) = 0, u(r, 0) = 0, diff(u(r, t), t) = -2}]

Why is there a difference between pdetest and algsubs for a PDE?
Shouldn't pdetest work the same as algsubs for the example below?

restart: with(PDEtools):




I have the following problem with the commands "Infinitesimals" and "InvariantSolutions". After using them to a system of firsst-order PDE's, the following message appears:


 Error, (in table["k"]) expected a request of prolongation w.r.t one of 2 independent variables; received a request w.r.t the (inexistent) 4th one

Does anybody know, what this message means ? I am a beginner with the commands "Infinitesimals" and "InvariantSolutions"...

Hi in trying to solve these coupled differential equations i get a weird error:


> t := diff(X(x), x) = -(1-6*R(x)^(1/2))^(1/2)*x*X(x)/(X(x)*x+R(x))^(1/2), diff(R(x), x) = (1-6*R(x)^(1/2))^(1/2)*x^2*X(x)/(X(x)*x+R(x))^(1/2);
/ (1/2)\
d \1 - 6 R(x) / x X(x)
--- X(x) = - -----------------------------,
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