Items tagged with pde

 

Hi all. I need to solve a large number of PDEs (partial differential equations) symbolically and simultaneously, to find the linearly independant answers for all of them, I use

ans := pdsolve({seq(PDE[i]=0,i=1..d)});

The PDEs are all linear first order and it is very easy to solve them one by one by hand, but in some cases I have 100 PDEs or more, so Maple is either very slow or doesn't work. For d=120, it was evaluating for hours without a result.

 

For example I have d=120 PDEs, and 200 variables. It works for d=30 of them (takes 13 minutes on my 16GB RAM  windows 7 computer). So if I do this:

ans1 := pdsolve({seq(PDE[i]=0,i=1..30)});

ans2 := pdsolve({seq(PDE[i]=0,i=31..60)});

ans3 := pdsolve({seq(PDE[i]=0,i=61..90)});

ans4 := pdsolve({seq(PDE[i]=0,i=91..120)});

Then how can I have only one vector of the linearly independent answers of all of them?

 

And in general, is Maple supposed to do this kind of calculations at all?

If yes, do you have any ideas on how to improve this procedure? 

If not, do you know in which software or programming package I can solve a large number of PDEs symbolically?

Your help is much appreciated. 

I'm trying to solve a system that contains the Laplace homogeneous equation and the boundary/initial conditions, thus i'm typing the following code:

> LAPLACE := (D[1, 2](u))(x, y)+(D[2, 2](u))(x, y) = 0;

            D[1, 2](u)(x, y) + D[2, 2](u)(x, y) = 0


> sys[1] := [LAPLACE, u*(x, 0) = 0, u(0, y) = 0, u(1, y) = 0, u(x, 1) = x^2*(1-x)];


[(D[1, 2](u))(x, y)+(D[2, 2](u))(x, y) = 0, u*(x, 0) = 0, u(0, y) = 0, u(1, y) = 0, u(x, 1) = x^2*(1-x)]

but when i use the command pdsolve(sys[1]) the message below appears:

"Error, (in pdsolve/sys/info) ambiguous input: the variables {u} and the functions {u(0, y), u(1, y), u(x, 1), u(x, y)} cannot both appear in the system"
 

So, it seems the declaration of the system isn't correct, but it's exactly how the tutorial of the maplesoft shows it. Could you please make clear what is a system of pde for maple and what is the correct tool for solving a system with boundary/initial conditions?

For the PDE, I can't seem to plot T' as the y-axis, it gives me the error, "Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct". Anyone knows what seem to be the problem? I am open to all ideas and would appreciate any help:)

fyp3.mw

Hi! 

Tried to solve the PDE below (q and p are time-dependent variabels, q(t),p(t)):

pde := diff(rho(t, q, p), t) = -(diff(rho(t, q, p), q))*p+(diff(rho(t, q, p), p))*(2*q+2);
          

pdsolve(pde, rho(t, q, p));
           

And got the answer: 

rho(t, q, p) = _F1(p^2+2*q^2+4*q, -(1/2)*sqrt(2)*arctan((q+1)*sqrt(2)*(1/sqrt(p^2)))+t)

But I'm not sure how to interpret the result. I understand that  _F1 is an arbitrary function, but then I get confused with the comma? I thought that I'd get a function of q and p, where they depend on t. 

Best regards
Sannis

 

Hello! 

For the last couple of days I've been trying really hard to solve the linear PDE 

dR/dt = -dRdH/dqdp + dRdH/(dpdq) . Where R is a function R(t,q(t),p(t)) and H is the hamiltonian H=  p^2/2 +q^2 +2*q .

(dH/dp= p and dH/dq= -2q-2), q and p depends on the time t, and I'm supposed to solve the PDE and then plot the gaussian distribution (2D). 

I tried doing this:

pde := diff(R(t, q1(t), p1(t)), t) = -(diff(R(t, q(t), p(t)), q(t)))*p(t)+(diff(R(t, q(t), p(t)), p(t)))*(-2*q(t)-2)

But pdsolve(pde) gives me:  "Error, (in pdsolve/info) the name of the indeterminate function must be given". 

When I change q(t) to q and p(t) to p I get:

R(t, q, p) = _F1(p^2-2*q^2-4*q, -(1/2)*ln(sqrt(2)*q+p+sqrt(2))*sqrt(2)+t)

And then I'm lost. How do I solve this PDE in maple? 

Thankful for any help 

 

 

with(DifferentialGeometry):with(JetCalculus):
DGsetup([x],[u],E,5);
vars≔x,u,u[1],u[1,1],u[1,1,1];
PDEtools[declare](Q(vars));
TotalDiff(Q(vars),x);
TotalDiff(u[1,1],x);

 

Hi everyone,

Recently I came across the total differentiation command in the PDEtools. For its

documentation, I used the following link

http://www.maplesoft.com/support/help/Maple/view.aspx?path=DifferentialGeometry/JetCalculus/TotalDiff

Unfortunately, when I try to replicate this it did not work as expected. I am getting the total derivative of the expression to be zero. I do not understand where I am going wrong.

You can find my code above. I am also attaching the screen shot of my maple file.

I would really appreciate if someone could help me out. Thanks for your help.


 

 

Hello everybody,

 

I want to solve this pde.the desire solution is V(r,z). three boundar conditions are written that two of them are related to rhe radial and one is related to the longitudinal coordinate.

I attached the solution for you. but this solution is derived by Matlab. Now, I just want to resolve it by Maple, but I couldn't reach it. Please let me know the correct way asap.

 

Thanks a lot.PDE.mw
 

NULL

NULL

restart 

Q := diff(V(r, z), r, r)+(diff(V(r, z), r))/r-V(r, z)/r^2+diff(V(r, z), z, z)+C/r = 0

diff(diff(V(r, z), r), r)+(diff(V(r, z), r))/r-V(r, z)/r^2+diff(diff(V(r, z), z), z)+C/r = 0

(1)

NULL

NULL

pdsolve(Q)

PDESolStruc(V(r, z) = _F1(r)*_F2(z)-(1/2)*(_C1/r+_C2*r+_C3*r*ln(r))*C/_C3, [{diff(diff(_F1(r), r), r) = _F1(r)*_c[1]+(-(diff(_F1(r), r))*r+_F1(r))/r^2, diff(diff(_F2(z), z), z) = -_F2(z)*_c[1]}])

(2)

NULL

 

NULL

NULL

``

``


 

Download PDE.mwPDE.mw

 

 

Hi all, I need a heep to solve 6 PDEs from the first order with initial and boundry conditions.

Here is the file PDE_with_IBC-BC.mwPDE_with_IBC-BC.mw

Hello there. I have a simple differential equation (diff(y(x), x)+1)*exp(y(x)) = 4 , in which I want to got a partial solution (find a value of constant) for y(1)=0. How do I do that? I've checked help on pdsolve function and it's too complicated for me to understand something. Examples do not contain anything such simple as that. Thanks in advance.

Hi guys! 

I have a PDE system. The mayority of the equations are equal to zero, but two of them are:

 

where a, b, c, d are CONSTANT parameters. I know that if a=b=d=c=1 the system is inconsistent. But I also know that if a=-1, b=d=0 and c=1 the system is consistent and exist the solution. I wanna know if there's a way to ask maple to find another selections of my parameter that make my PDE consistent and what it's the solution for that selection of a,b,c,d. 

Here's my PDE system (sys2). 

test.mw

thank you so much for your time! 

I am trying to solve a system of equations of motion of gravitational field and in this way, I deal with a second order differential equation containing Dirac delta function as follows:

Eq9 := -(l[f]^2/l[g]^2+2)*(diff(G(r, t), r, r)-2*(diff(G(r, t), r))/r)+l[f]^2*(diff(F(r, t), r, r)-2*(diff(F(r, t), r))/r)/l[g]^2+2*l[f]^2*(m^2*l[f]^2-3)*(G(r, t)/r^2-F(r, t)/r^2)/l[g]^2 = l[g]*E*exp(Pi*t*l[f]^2*(1-2*kappa)/l[g]^2)*Dirac(t)*Dirac(r)*Dirac(z)

and

Eq10 := diff(G(r, t), r, r)-2*(diff(G(r, t), r))/r-2*kappa*(diff(F(r, t), r, r)-2*(diff(F(r, t), r))/r)-(2*(m^2*l[f]^2-3))*(G(r, t)/r^2-F(r, t)/r^2) = l[g]*E*exp(Pi*t*l[f]^2*(1-2*kappa)/l[g]^2)*Dirac(t)*Dirac(r)*Dirac(z)

 want to solve these equations with MAPLE software symbolically.
Can anyone guide me in this way, please?

I had problems plotting the solutions of my PDE with the derivative as the axis. Anyone knows what went wrong?

p1 := pds:-plot(diff(f(x,y),y), y = 0 .. 10, x = 0, numpoints = 100)

I seem to be getting a plot of y=0. Any help would be greatly appreciated:))

 

fyp2.mw

I know there is some code to compute the symmetry of pde, but i want to compute the symmetry of some differential expression, as f(x,t,ux,ut).

The difference is that when solve the infinitesimal, we don't have the identity f(x,t,ux,ut)=0, we just take each variable in the jet space as independent.

Is there any package to do that?

help and thanks!

I have a system of pde as follow,

PDE := [(x*y+1)*(diff(f(x, y), y, y, y))+(x+(3/4)*f(x, y))*(diff(f(x, y), y, y))-(1/2)*(diff(f(x, y), y))^2+T(x, y) = (1/4)*x*(diff(f(x, y), y))*(diff(diff(f(x, y), y), x))-(1/4)*x*(diff(f(x, y), x))*(diff(f(x, y), y, y)), (x*y+1)*(diff(T(x, y), y, y))/(.733)+(x/(.733)+(3/4)*f(x, y))*(diff(T(x, y), y)) = (1/4)*x*(diff(f(x, y), y))*(diff(T(x, y), x))-(1/4)*x*(diff(f(x, y), x))*(diff(T(x, y), y))]


sys_ode := diff(g(y), y, y, y)+(3/4)*g(y)*(diff(g(y), y, y))-(1/2)*(diff(g(y), y))^2+h(y) = 0, (diff(h(y), y, y))/(.733)+(3/4)*g(y)*(diff(h(y), y)) = 0

ics := g(0) = 0, h(0) = 1, (D(g))(10) = 0, g(10) = 0, h(10) = 0

sol2 := dsolve([sys_ode, ics], numeric)

BC := {T(0, y) = h(y), T(x, 0) = 1, T(x, 10) = 0, f(0, y) = g(y), f(x, 0) = 0, f(x, 10) = 0, (D[2](f))(x, 0) = 0}

pds := pdsolve(PDE, BC, numeric)

module() ... end module

pds:-plot(T, y = 0 .. 10, x = 0);

Error, (in pdsolve/numeric/plot) unable to compute solution for x<HFloat(0.0):
solution becomes undefined, problem may be ill posed or method may be ill suited to solution

When I try to use the solution of the Ode as the boundary condition for PDE, by subbing g(y) and h(y) into BC. The plot returns me the error. Anyone knows the reason behind this and how to solve? Any help would be really greatly appreciated. Thanks

Hi,

 

I have a PDE which I would like to group certain terms in common. They are all general functions and do not all share variables in common.

It is easier to explain in the script attached.

Any guidance anyone can offer would be greatly appreciated. 

Thank you 

 

question3.mw

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