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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,

 

 

 

hi .may every one help me for pdsolve this differential equations?

all initial boundary condition are zero

thanks...

pdeSol_(1).mw

 

#
# Define some parameters
#
  sigma := 10; N := 0; beta := 1; alpha := 1; PDE1 := diff(w(X, theta, t), X, X, X, X)+2*alpha^2*(diff(w(X, theta, t), theta, theta, X, X))+alpha^4*(diff(w(X, theta, t), theta, theta, theta, theta))-N*(diff(w(X, theta, t), X, X))+diff(w(X, theta, t), t, t)-beta*w(X, theta, t)-sigma = 0

10

 

0

 

1

 

1

 

diff(diff(diff(diff(w(X, theta, t), X), X), X), X)+2*(diff(diff(diff(diff(w(X, theta, t), X), X), theta), theta))+diff(diff(diff(diff(w(X, theta, t), theta), theta), theta), theta)-10+diff(diff(w(X, theta, t), t), t)-w(X, theta, t) = 0

(1)

#
# Define the PDES
#
  PDEs:= { diff(w(X, theta, t), X, X, X, X)+2*alpha^2*(diff(w(X, theta, t), theta, theta, X, X))+alpha^4*(diff(w(X, theta, t), theta, theta, theta, theta))-N*(diff(w(X, theta, t), X, X))+diff(w(X, theta, t), t, t)-beta*w(X, theta, t)-sigma = 0
   };

{diff(diff(diff(diff(w(X, theta, t), X), X), X), X)+2*(diff(diff(diff(diff(w(X, theta, t), X), X), theta), theta))+diff(diff(diff(diff(w(X, theta, t), theta), theta), theta), theta)-10+diff(diff(w(X, theta, t), t), t)-w(X, theta, t) = 0}

(2)

#
# Set of boundary conditions at x=1.
#
   bcs1:= { D[1](w)(1,theta, t) = 0,
              w(1,theta, t) = 0
         };

{w(1, theta, t) = 0, (D[1](w))(1, theta, t) = 0}

(3)

#
# Set of boundary conditions at x=0
#
  bcs2:= {    w(0,theta, t)=0,
           D[1](w)(0,theta, t)=0
         };

{w(0, theta, t) = 0, (D[1](w))(0, theta, t) = 0}

(4)

#
# Set of boundary conditions at t=0
#
  bcs3:= { w(x,theta,0)=0,
          
           D[2](w)(x,theta,0)=0 };
           

{w(x, theta, 0) = 0, (D[2](w))(x, theta, 0) = 0}

(5)

 


  pdsolve( PDEs, `union`(bcs1, bcs2, bcs3), numeric);

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

 

 

 

Download pdeSol_(1).mw

i have runed below system of PDES as:



c := 3*10^8;
                           
hbar := 0.105457148e-33;
                             
kB := 0.13806503e-22;
                                
epsilon0 := 0.885418782e-11;
                                                        
timeunit := 1;
                             
g := 1*timeunit;
                            
t0 := 0.10e-4/g;
                           
k := 5/(0.1e10*g);
                                                          
td := 0.10e-4/g;
B := 1;
                            
L := 0.1e-2;
                           
OD := 0.1e7;
              
eta := g*OD/(2*L);
                                 
                       
Omegap0 := .1*g;
      

Omegac(z):=(1e7*B*g)/(sqrt(1+((z-L)/(0.2*L))^(2)));


                 
PDE1 := diff(rho31(t, z), t) = -(1/2)*g*rho31(t, z)+(.5*I)*Omegac(z)*rho21(t, z)+(.5*I)*Omegap(t, z);
                        
PDE2 := diff(rho21(t, z), t) = (.5*I)*Omegac(z)*rho31(t, z);
                                                          
         
PDE3 := diff(Omegap(t, z), t) = -c*(diff(Omegap(t, z), z))+I*c*eta*rho31(t, z);
       

IBC := {Omegap(0, z) = 0, Omegap(t, 0) = Omegap0*exp(-((t-t0)/k)^2), rho21(0, z) = 0, rho31(0, z) = 0};
 
                              
pds := pdsolve({PDE1, PDE2, PDE3}, IBC, numeric, time = t, range = 0 .. 0.1e-2);
                      

 

 

every things is ok but I don't know how can i plot rho31, rho21 and Omegap in 2D or 3D plot.

I have tried

but i see the bellow error:

Error, (in pdsolve/numeric/plot) unable to compute solution for t>INFO["failtime"]:
unable to store -37500000000000000*I when datatype=float[8]

Please help me to solve the error?

Thanks

hi...please help me for solve this nonlinear equations with pdsolve

thanksoffcenter2.mw

La := .25; Lb := 0.1e-1

h := 0.4e-2

rho := 7900

E := 0.200e12

nu := .3

ve := 5

g := 9.8

M := .5

Z0 := 0.1e-2

K := 5/6

C := sqrt(E/rho)

NULL

 

PDE[1] := diff(u(x, t), x, x)+(diff(w(x, t), x))*(diff(w(x, t), x, x)) = (diff(u(x, t), t, t))/C^2

diff(diff(u(x, t), x), x)+(diff(w(x, t), x))*(diff(diff(w(x, t), x), x)) = 0.3949999999e-7*(diff(diff(u(x, t), t), t))

(1)

PDE[2] := K*(diff(phi(x, t), x)+diff(w(x, t), x, x))/(2*(1+nu))+(diff(w(x, t), x))*(diff(u(x, t), x, x))+(diff(u(x, t), x))*(diff(w(x, t), x, x))+(3/2)*(diff(w(x, t), x, x))*(diff(w(x, t), x))^2 = (diff(w(x, t), t, t))/C^2

.3205128205*(diff(phi(x, t), x))+.3205128205*(diff(diff(w(x, t), x), x))+(diff(w(x, t), x))*(diff(diff(u(x, t), x), x))+(diff(u(x, t), x))*(diff(diff(w(x, t), x), x))+(3/2)*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))^2 = 0.3949999999e-7*(diff(diff(w(x, t), t), t))

(2)

 

PDE[3] := diff(phi(x, t), x, x)-6*K*(diff(w(x, t), x)+phi(x, t))/(h^2*(1+nu)) = (diff(phi(x, t), t, t))/C^2

diff(diff(phi(x, t), x), x)-240384.6154*(diff(w(x, t), x))-240384.6154*phi(x, t) = 0.3949999999e-7*(diff(diff(phi(x, t), t), t))

(3)

 

 

#####################################

(4)

at x= La

PDE[a1] := diff(u(x, t), x)+(1/2)*(diff(w(x, t), x))^2-M*(g-(diff(u(x, t), t, t))-Z0*(diff(phi(x, t), t, t)))/(E*Lb*h) = 0

diff(u(x, t), x)+(1/2)*(diff(w(x, t), x))^2-0.6125000000e-6+0.6250000000e-7*(diff(diff(u(x, t), t), t))+0.6250000000e-10*(diff(diff(phi(x, t), t), t)) = 0

(5)

PDE[a2] := diff(phi(x, t), x)-12*M*Z0*(g-(diff(u(x, t), t, t))-Z0*(diff(phi(x, t), t, t)))/(E*Lb*h^3) = 0

diff(phi(x, t), x)-0.4593750000e-3+0.4687500000e-4*(diff(diff(u(x, t), t), t))+0.4687500000e-7*(diff(diff(phi(x, t), t), t)) = 0

(6)

PDE[a3] := w(x, t) = 0

w(x, t) = 0

(7)

NULL

############################################

``

at x=0 NULL

(8)

PDE[b1] := u(x, t) = 0 

PDE[b2] := w(x, t) = 0

PDE[b3] := diff(phi(x, t), x) = 0

diff(phi(x, t), x) = 0

(9)

################################################

at t=0 for x= [0,La]

u(x, t) = 0

u(x, t) = 0

(10)

w(x, t) = 0

w(x, t) = 0

(11)

phi(x, t) = 0

phi(x, t) = 0

(12)

diff(phi(x, t), t) = 0

diff(phi(x, t), t) = 0

(13)

diff(w(x, t), t) = 0

diff(w(x, t), t) = 0

(14)

diff(phi(x, t), t, t) = 0

diff(diff(phi(x, t), t), t) = 0

(15)

diff(w(x, t), t, t) = 0

diff(diff(w(x, t), t), t) = 0

(16)

######################################################

at t=0 for x= [0,La)

diff(u(x, t), t) = 0

diff(u(x, t), t) = 0

(17)

diff(u(x, t), t, t) = 0

diff(diff(u(x, t), t), t) = 0

(18)

###################################################

at t=0 for x=La

NULL

diff(u(x, t), t) = -ve

diff(u(x, t), t) = -5

(19)

diff(u(x, t), t, t) = g

diff(diff(u(x, t), t), t) = 9.8

(20)

NULL

NULL

 

Download offcenter2.mw

Hi

I need to solve below integro-differential equation

0.3846153846*(diff(F(x, y), y, y))+diff(F(x, y), x)-(diff(w(x), x, x))*y-(1/2)*(int(diff(F(x, y), x), y = -1 .. 1))+diff(F(x, y), x, x)-(diff(w(x), x, x, x))*y-(1/2)*(int(diff(F(x, y), x, x), y = -1 .. 1))

The solution is as follows:

(diff(w(x), x))*y-_C1*y/exp(x)-(1923076923/5000000000)*_c[2]*x*y+_C2*y+(1/6)*_c[2]*y^3+_C4*y+_F1(x)

 

The parameters _C1, _C2, c[2], C4 are functions of x, or functions of y? Or these parameters are constant numbers? 

In addition to, is it reasonable to use C *y instead of _C2*y+_C4*y ?

 

Thank you

I have the PDE u_{xx}+u_{yy} = 1 with BC: u|_{x^2+y^2=1} =0 ;

 

how to write down the command of the BC in solving this PDE?, btw can I make maple show me how to solve this PDE analytically?

 

Thanks in advance.

 

Here are the lines that I wrote so far:

pde := diff(u(x, y), x, x)+diff(u(x, y), y, y) = 1;

ans := pdsolve(pde)

 

how to add the BC correctly to pdsolve? I am not sure how to write the condition x^2+y^2=1 and that u will get a value on this boundary.

 

hi .please help me for solve this equations.

bbb2.mw

restart; d[11] := 1; mu[11] := 1; q[311] := 1; d[33] := 1; mu[33] := 1; a[11] := 1; e[311] := 1; a[33] := 1; A := 1; g[111111] := 1; c[1111] := 1; g[113113] := 1; f[3113] := 1; beta[11] := 1; `&Delta;T` := 1; II := 1; L := 1

J := d[11]*(diff(Phi(x, z), x, x))+mu[11]*(diff(psi(x, z), x, x))+q[311]*(diff(w(x), x, x))+d[33]*(diff(Phi(x, z), z, z))+mu[33]*(diff(psi(x, z), z, z));

diff(diff(Phi(x, z), x), x)+diff(diff(psi(x, z), x), x)+diff(diff(w(x), x), x)+diff(diff(Phi(x, z), z), z)+diff(diff(psi(x, z), z), z)

(1)

B := a[11]*(diff(Phi(x, z), x, x))+d[11]*(diff(psi(x, z), x, x))+e[311]*(diff(w(x), x, x))+a[33]*(diff(Phi(x, z), z, z))+d[33]*(diff(psi(x, z), z, z));

diff(diff(Phi(x, z), x), x)+diff(diff(psi(x, z), x), x)+diff(diff(w(x), x), x)+diff(diff(Phi(x, z), z), z)+diff(diff(psi(x, z), z), z)

(2)

R := A*(g[111111]*(diff(u[0](x), x, x, x, x))-c[1111]*(diff(u[0](x), x, x)+(1/2)*(diff((diff(w(x), x))^2, x)))+e[311]*(diff(diff(Phi(x, z), z), x))+q[311]*(diff(diff(psi(x, z), z), x)));

diff(diff(diff(diff(u[0](x), x), x), x), x)-(diff(diff(u[0](x), x), x))-(diff(w(x), x))*(diff(diff(w(x), x), x))+diff(diff(Phi(x, z), x), z)+diff(diff(psi(x, z), x), z)

(3)

S := -II*g[111111]*(diff(w(x), x, x, x, x, x, x))-II*c[1111]*(diff(w(x), x, x, x, x))+A*g[113113]*(diff(w(x), x, x, x, x))-A*f[3113]*(diff(diff(Phi(x, z), z), x, x))-A*(c[1111]*(diff(u[0](x), x, x)+(1/2)*(diff((diff(w(x), x))^2, x)))+e[311]*(diff(diff(Phi(x, z), z), x))+q[311]*(diff(diff(psi(x, z), z), x)))*(diff(w(x), x))-A*(diff(w(x), x, x))*(c[1111]*(diff(u[0](x), x)+(1/2)*(diff(w(x), x))^2)+e[311]*(diff(Phi(x, z), z))+q[311]*(diff(psi(x, z), z))-beta[11]*`&Delta;T`);

-(diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x))-(diff(diff(diff(Phi(x, z), x), x), z))-(diff(diff(u[0](x), x), x)+(diff(w(x), x))*(diff(diff(w(x), x), x))+diff(diff(Phi(x, z), x), z)+diff(diff(psi(x, z), x), z))*(diff(w(x), x))-(diff(diff(w(x), x), x))*(diff(u[0](x), x)+(1/2)*(diff(w(x), x))^2+diff(Phi(x, z), z)+diff(psi(x, z), z)-1)

(4)

dsys := {B, J, R, S}; BCS := {D@@2*w(0) = 0, D@@2*w(L) = 0, Phi(x = 0) = 0, Phi(x = L) = 0, Phi(z = -(1/2)*h) = 0, Phi(z = (1/2)*h) = 0, psi(x = 0) = 0, psi(x = L) = 0, psi(z = -(1/2)*h) = 0, psi(z = (1/2)*h) = 0, w(x = 0) = 0, w(x = L) = 0, u[0](x = 0) = 0, u[0](x = L) = 0, (D(w))(0) = 0, (D(w))(L) = 0, (D(u[0]))(0) = 0, (D(u[0]))(L) = 0}

{D@@2*w(0) = 0, D@@2*w(L) = 0, Phi(x = 0) = 0, Phi(x = L) = 0, Phi(z = -(1/2)*h) = 0, Phi(z = (1/2)*h) = 0, psi(x = 0) = 0, psi(x = L) = 0, psi(z = -(1/2)*h) = 0, psi(z = (1/2)*h) = 0, w(x = 0) = 0, w(x = L) = 0, u[0](x = 0) = 0, u[0](x = L) = 0, (D(w))(0) = 0, (D(w))(L) = 0, (D(u[0]))(0) = 0, (D(u[0]))(L) = 0}

(5)

dsol5 := dsolve(dsys, numeric)

Error, (in dsolve/numeric/process_input) missing differential equations and initial or boundary conditions in the first argument: dsys

 

NULL

NULL

NULL

if former equations are not solvable , please help me for another way, in which at first two equation solve..in this way in equation [J and B] assume that q[311]=e[311]=0 and dsolve perform to find Φ and  ψ

after by finding Φ and  ψ is use for detemine w and u0

please see attached file below[bbb2_2.mw]

bbb2_2.mw

Download bbb2.mw

I have the following PDE system steaming from Flash Photolysis:

pdesys := [diff(J(x, t), x) = varepsilon*J(x, t)*C(x, t), diff(C(x, t), t) = phi*varepsilon*J(x, t)*C(x, t)]

when I use pdsolve(pdesys,[J,C]) I get:

{C(x, t) = 0, J(x, t) = _F1(t)}, {C(x, t) = _F1(x)*_C1, J(x, t) = 0}

The solution appears to be either C(x,t) = 0 or J(x,t) = 0. This are the obvious solutions (0 = 0). I have the analytical solution to this PDE system where neither C(x,t) nor J(x,t) are 0.

How to solve this system in maple? Thanks.

 

Hi evrey ones in pdsolve we have these commande to use U(x,t) 

> U:= subs(pds:-value(output=listprocedure), u(x,t));

  id like to get du(x,t)/dt

i tried these  

U:= subs(pds:-value(output=listprocedure), du(x,t)/dt);  but is not work 

thank you 

 

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