Items tagged with pdsolve

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

 

I have the following code in Maple 13:

SYS := {diff(T(x, t), t) = diff(T(x, t), x, x)};
IBC := {T(1, t) = 0, T(x, 0) = 1, (D[1](T))(0, t) = -exp(t)};
SOL := pdsolve(SYS, IBC, numeric, time = t, timestep = 1/10);
R := SOL:-value(output = listprocedure); temperature := subs(R, T(x, t));

It integrates the heat equation in the interval x=0..1 and it seems to work ok.
However, I have problems trying to obtain the temperature derivative at the boundaries (this is at x=0 and x=1). I'm using different commands and it seems the derivative is evaluated ok inside the domain but not at the boundaries.
If I try
fdiff(temperature(x, t), [x], {x = 1,t=0.5});

or

evalf((D[1](temperature))(1, .5));

I don't get any numerical answer. Any idea how I could obtain the value of the derivative at the boundaries?

Thanks in advance,

Javier

 




 

 

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

 

 

For my fdiff graph, it seems that the cirtical points appear to be jaggered or not smooth. Anyone nows what seem to be the problem? i tried increasing the numpoints but it did not work:( I am open to all opinions. Thanks:)

 

fyp2.mw

Hi all. I'm using pdsolve to find linearly independent solutions for two partial differentioal equations. I can solve them seperatly by "pdsolve", but when I try to solve them at the same time to get answers that fit in both of the eauations, I get an error message. I need to be able to solve them as a set of equations, as I have bigger examples. Here are the equations and outputs: 

PDE[1] := diff(f(theta[I], theta[A], theta[B], theta[AB]), theta[AB]);

PDE[2] := -(diff(f(theta[I], theta[A], theta[B], theta[AB]), theta[I]))+diff(f(theta[I], theta[A], theta[B], theta[AB]), theta[A])+diff(f(theta[I], theta[A], theta[B], theta[AB]), theta[B]);

pdsolve(PDE[1] = 0)  ----->  f(theta[I], theta[A], theta[B], theta[AB]) = _F1(theta[I], theta[A], theta[B])

pdsolve(PDE[2] = 0) ----->  f(theta[I], theta[A], theta[B], theta[AB]) = _F1(theta[I]+theta[A], theta[I]+theta[B], theta[AB])

pdsolve({seq(PDE[i] = 0, i = 1 .. 2)}) ---->  Error, (in PDEtools:-casesplit) too many levels of recursion

Why doesn't it produce the answer, although I know that it must be:

f(theta[I], theta[A], theta[B], theta[AB])=_F1(theta[I]+theta[A], theta[I]+theta[B])

Can somebody of Maple users execute the following command

restart; pdsolve({diff(w(x, y, z), x)+diff(w(x, y, z), y, y)+2*(diff(v(x, y, z), x)-(diff(u(x, y, z), y))-2*w(x, y, z)) = diff(w(x, y, z), z, z), 3*(diff(u(x, y, z), x, x))+2*(diff(u(x, y, z), y, y))+2*(diff(v(x, y, z), x, y))+2*(diff(w(x, y, z), y)) = diff(u(x, y, z), z, z), 3*(diff(v(x, y, z), y, y))+2*(diff(v(x, y, z), x, x))+2*(diff(u(x, y, z), x, y))-2*(diff(w(x, y, z), x)) = diff(v(x, y, z), z, z)}, {u(x, y, z), v(x, y, z), w(x, y, z)})

restart; pdsolve({diff(w(x, y, z), x)+diff(w(x, y, z), y, y)+2*(diff(v(x, y, z), x)-(diff(u(x, y, z), y))-2*w(x, y, z)) = diff(w(x, y, z), z, z), 3*(diff(u(x, y, z), x, x))+2*(diff(u(x, y, z), y, y))+2*(diff(v(x, y, z), x, y))+2*(diff(w(x, y, z), y)) = diff(u(x, y, z), z, z), 3*(diff(v(x, y, z), y, y))+2*(diff(v(x, y, z), x, x))+2*(diff(u(x, y, z), x, y))-2*(diff(w(x, y, z), x)) = diff(v(x, y, z), z, z)}, {u(x, y, z), v(x, y, z), w(x, y, z)})

Error, (in simplify/normal) Maple was unable to allocate enough memory to complete this computation.  Please see ?alloc

 

 

 

in Maple 2016.1.1 on a powerful comp and report the obtained result as an answer to the question?
 That would be very kind of her/him. Thanks in advance. 

Download pdsolve.mw

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

Hello, 

I have a PDE system. When I use pdsolve it gets me the messege " pdsolve->Warning: System is inconsistent". Is there a way I can see which equations breaks the system down? 
For this system, it's difficult to see from ayeball where the problem is. 
Thank you! 

test.mw

hi

please help to me for solve this equation via pdsolve?

thanks

dsove2.mw

restart

f := 1; k := 1; h := 1

PDE := diff((diff(rho*H(rho, z), rho))/rho, rho)+diff(H(rho, z), z, z)+k^2*H(rho, z) = f

-(H(rho, z)+rho*(diff(H(rho, z), rho)))/rho^2+(2*(diff(H(rho, z), rho))+rho*(diff(diff(H(rho, z), rho), rho)))/rho+diff(diff(H(rho, z), z), z)+H(rho, z) = 1

(1)

NULL

NULL

NULL

NULL

sol3 := dsolve([PDE, (D[2](H))(rho, -h) = 0, (D[2](H))(rho, 0) = 0], H(rho, z))

NULL



Download dsove2.mw

 

 

 


Please, I need assistance with this problem.

Here is the problem I am trying to solve:

restart:
with(plots):
with(LinearAlgebra):
with(PDEtools):
with(Student):

myPDE1 := D11*diff(w(x,y), x$4) + 2*(D12+2*D66)*diff(w(x,y), y$4) + D22*diff(w(x,y), x$2, y$2) - G*diff(w(x,y), x,y)= 0;

pdsolve(myPDE1);

pdsolve(myPDE1, build);

"Boundary conditions";
"(Note:the domain for the problem is a rectangle)";
bc1 := w(0,y) = 0; # @ x=0 edge;
bc2 := w(a,y) = 0;  # @ x=a edge;
bc3 := w(x,0) = 0; # @ y=0 edge;
bc4 := w(x,b) = 0; # @ y=b edge;
bcx1 := -D11*D[2](w)(0,y) - D12*D[2](w)(0,y) = 0; # @ x=0 edge;
bcx2 := -D11*D[2](w)(a,y) - D12*D[2](w)(a,y) = 0; # @ x=a edge;
bcy1 := -D12*D[2](w)(x,0) - D22*D[2](w)(x,0) = 0; # @ y=0 edge;
bcy2 := -D12*D[2](w)(x,b) - D22*D[2](w)(x,b) = 0; # @ y=b edge;

sol := [myPDE1, bc1, bc2, bc3, bc4, bcx1, bcx2, bcy1, bcy2];

pdsolve(sol);

"Note:
and D11, D12, D22, D66 and G are constant.
The intention is to find the critical value for G"

I need help with how I can handle the boundary conditions for the problem. Thanks a million.

hi...how i can pdsolve this equation numerically or analyticlly?

this equation is time-fractional  equation with generalized Cattaneo model

where

 

 is the fractional derivative operator considered in the
Caputo sense.

 

FRACTION.mw

restart

k := 1; -1; rho := 1; -1; h := 1; -1; alpha := 2-Upsilon; -1; 0 < Upsilon and Upsilon <= 1

0 < Upsilon and Upsilon <= 1

(1)

k*(diff(T(z, t), z, z)) = rho*(diff(T(z, t), [`$`(t, alpha)]))

diff(diff(T(z, t), z), z) = diff(T(z, t), [`$`(t, 2-Upsilon)])

(2)

k*(diff(T((1/2)*h, t), z)) = 1:

k*(diff(T((-h)*(1/2), t), z)) = 0:

T(z, 0) = 0

T(z, 0) = 0

(3)

NULL



Download FRACTION.mw

 

Hello everybody!

Please help me to solve the attached partial differential equation. I am getting an error. I do have its analytical solution and that works fine.

The error is as follows
Error, (in pdsolve/numeric/plot) unable to compute solution for t>HFloat(0.0):
solution becomes undefined, problem may be ill posed or method may be ill suited to solution

The worksheet is attached hereshortsngle.mw

I am trying to solve a PDE using pdsolve-numeric. I am getting an error related to boundary conditions.
Please see the follwing worksheet and suggest me some solutions

pdsolve.mw

Hello Everyone,

May I ask you about this  "Error,   (in pdsolve/numeric/process_PDEs)  number of dependent variables and number of PDE must be the same". Does anyone have idea about solving linear instability equation (flow inside pipe, oscillating flow) ?

Thank you,

 

 

 

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