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Please help me.I don't know how to achieve the following iteration relation by maple code.iterative relationship

 

 

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

Hy Prof.

Please help me or guide me to get idea to solve Nonlinear coupled PDEwith MAPLE.Dr.Sam Dao could please help me as I saw your YOUTUBE lecturer which very helpful to me and please give some idea about my topic.

pde[1] := diff(u(x, t), t)-D(diff(u(x, t), x, x)) = alpha*u(x, t)*(1-v(x, t))

pde[2] := diff(v(x, t), t)-E(diff(v(x, t), x, x)) = beta*v(x, t)*(1-u(x, t))

Thanks in advance and answer is highly appricaited 

i have 2 PDE equations with some boundary conditions,maple get me errors, what should i do ? please help
how can i make correction in my system or boundary to have a solution ?

Download pde2.mw

tnx in advance

Can some one help me for converting three or two coupled pdes to odes using Lie group or any other method in maple

 

 

                                                                      

                                                                   

                                                                     

                                                                        

                                                                      

 

I thought about the following PDE:

 

EDIT: The u(0,t) is not a typo! It is really meant to be part of the PDE!

 

Latex/Matjax: $$\dfrac{\partial u(x,t)}{\partial t}=\alpha \dfrac{\partial^2 u(x,t)}{\partial x^2}+u(x=0,t).$$

Maple: diff(u(x,t),t)=alpha*diff(u(x,t),x$2)+u(0,t)

 

 

How can i determine the symmetries of this PDE with Maple?

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 all,

 

Please help me with this question. I want to solve a PDE by Maple.

restart

A := 5;

5

(1)

B := 9

9

(2)

c := 1

1

(3)

``

``

``

eq := diff(u(x, t), t, t)-c^2*(diff(u(x, t), x, x));

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

(4)

 

dsolve({eq, u(0, t) = A, u(1, t) = B, u(x, 0) = 0, (D(u))(x, 0) = sin(x)}, u(x, t))

Error, (in evalapply/D) too many variables for the derivative of a function of only one variable in D(u)(x, 0)

 

``

``

``

 

Download SolvePDE.mwSolvePDE.mw

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; `ΔT` := 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]*`ΔT`);

-(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

vz := 2*(-eta^2+1);

D_im := .22;

r0 := 1;

pde := diff(vz*Y(eta, z), z)-D_im*((diff(eta*(diff(Y(eta, z), eta)), eta))/eta+diff(Y(eta, z), `$`(z, 2)))/r0 = 0;

pde := expand(%);

ibc := [Y(1, z) = 0, (D[1](Y))(0, z) = 0, Y(eta, 0) = 1, (D[2](Y))(eta, 0) = 0];

sol := pdsolve(pde, ibc, numeric, time = z, range = 0 .. 1);

pds := sol:-value(z = 0, output = listprocedure);

sol:-plot(z = 0.1e-3, numpoints = 50, color = blue, view = 0 .. 1)

So I was trying to solve this conservation equation for the radial coordinate eta and the z coordinate being treated as time. The flow is in z direction. Now unfortunately it is diverging. Not sure why though. What am I doing wrong?

I am currently working on FDM ,i have 2 coupled nonlinear pde ,i need help in solving these equation using maple code.

> restart:

> alias(f=f(tau,eta), theta=theta(tau,eta));

 

>

 

> PDE1:=S*diff(f,tau,eta)=eta^2*diff(f,eta)^2+(6*eta^2-2*f*eta)*diff(f,eta)+(6*eta^3-f*eta)*diff(f,eta,eta)-eta^4*diff(f,eta,eta,eta);

 

> PDE2:=eta^4*diff(theta,eta,eta)+2*eta^3*diff(theta,eta)-Pr*(f*eta^2*diff(theta,eta)+S*diff(theta,tau))=0;

 

I'm trying to solve a 2nd order system of pde's with couplded BC but it gives me the following error

Error, (in pdsolve/numeric) initial/boundary conditions must be defined at one or two points for each independent variable

Here is the code

> T01 := 273; T02 := 26; L1 := .1; L2 := .2; h1 := 100; h2 := 200; k1 := 1; k2 := 2; rho1 := 1000; rho2 := 2000; c1 := 0.1e6; c2 := 0.2e6; alpha1 := 1; alpha2 := 2

> PDE := {diff(T1(x, t), t) = (diff(T1(x, t), x, x))/alpha1, diff(T2(x, t), t) = (diff(T2(x, t), x, x))/alpha2}

> IBC:={k1*(D[1](T1))(L1, t) = k2*(D[1](T2))(L1, t), T1(L1, t) = T2(L1, t), T1(x, 0) = T02, T2(x, 0) = T02, (D[1](T1))(0, t) = -h1*(T1(0, t)-T01)/k1, (D[1](T2))(L1+L2, t) = h2*(T2(L1+L2, t)-T02)/k2}

> pds := pdsolve(PDE, IBC, numeric)

Its basically a 1D heat equation in a 2 layers plate with conduction BC on both sides

I am currently working on FDM ,i have 2 coupled nonlinear pde ,i need help in solving these equation using maple code.

> restart:

> alias(f=f(tau,eta), theta=theta(tau,eta));

 

>

 

> PDE1:=S*diff(f,tau,eta)=eta^2*diff(f,eta)^2+(6*eta^2-2*f*eta)*diff(f,eta)+(6*eta^3-f*eta)*diff(f,eta,eta)-eta^4*diff(f,eta,eta,eta);

 

> PDE2:=eta^4*diff(theta,eta,eta)+2*eta^3*diff(theta,eta)-Pr*(f*eta^2*diff(theta,eta)+S*diff(theta,tau))=0;

 

Hi guys, I'm currently having a lot of trouble with Maple and can't seem to get stuff to work. I have the task of solving and modelling the Klien Gordon equation, with a chosen potential. The equation I'm trying to solve is:

> KGE := diff(psi(x, t), x, x)-(diff(psi(x, t), t, t))-12*psi(x, t)^5+10*psi(x, t)^4+6*psi(x, t)^3-3*psi(x, t)^2-psi(x, t) = 0   

I'm doing this by changing the pde into an ode via a transformation 

>tr := {t = tau, x = c*tau+z, psi(x, t) = U(z)}

>ode1 := dchange(tr, KGE, [z, tau, U(z)])

 >ode1 := collect(ode1, diff(U(z), z, z))

>c := 1/4

>ode2 := subs({U(z) = U, diff(U(z), z, z) = V(U)*(diff(V(U), U))}, ode1)

>sol := dsolve({ode2, V(0) = 0}, V(U))

>sol1:= sol[2]

>z := -c*t+x = int(1/rhs(sol2), U)

>solwave := psi(x, t) = solve(z, U)

 

I then checked if my solution, solwave actually solved the pde via pdetest(solwave,KGE) and it did. Hence this is what I took as one of the kinks. Although the kink solution looks hideous and I have no idea how to try and take the limit as x goes to infinity, as to show it tends to a vacuum of the potential. I've tried taking the limit but all Maple does is replace all the x with infinity signs... 

I then tried animating it to see if it worked, but it just looks wrong, there are breaks within the curve and also very random spikes which I cannot explain at all.. 

I tried this code exactly for the Sine Gordon equation and it works perfectly, it just all goes wrong when I try to change the potential. 

Here is a picture of the frame: 

as you can see it has spikes.. and breaks in the curve as well

----------------------------------------------------------------------------------------------

Another issue I had was with dealing with the potential on it's own, every time I try inputting  

>1/2(u^2)(1-u)^2(1+2u)^2  

into maple it changes the expression into something completely different and wrong, it somehow comes out with an exponential of 8.. This is what I get:

(1/2)*(u(1-u))(1+2*u)^8

 

----------------------------------------------------------------------------------------------

 

I also have a problem integrating, I try and plug in a value, i.e. 

>int(1/(x(1-x))(1+2*x), x)

but all this does is show me what I inputted but with a integral sign...

I'm very very new to Maple and have spent over a week doing this, but it just isn't working out at all :( Please help!! 

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