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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!! 


with(PDEtools, casesplit, declare)
``

L := 1651.12; m := 3205.12; r1 := .1875; r2 := 2; z1 := 0; z2 := 12; ld := 4.5

NULL

declare(u(r, z), w(r, z))``

with(DEtools, gensys)

rr := (L+2*m)*(diff(u(r, z), r))+L*(diff(w(r, z), z))+L*u(r, z)/r

zz := L*(diff(u(r, z), r))+(L+2*m)*(diff(w(r, z), z))+L*u(r, z)/r

rz := m*(diff(u(r, z), z))+m*(diff(w(r, z), r))

BCS := {rr(r1, ld) = 0, rz(r1, z) = T, w(r, 0) = 0, zz(r, z2) = 0}

{3205.12*(diff(u(r, z), z))(.1875, z)+3205.12*(diff(w(r, z), r))(.1875, z) = T, 8061.36*(diff(u(r, z), r))(.1875, 4.5)+1651.12*(diff(w(r, z), z))(.1875, 4.5)+1651.12*(u(r, z))(.1875, 4.5)/r(.1875, 4.5) = 0, 1651.12*(diff(u(r, z), r))(r, 12)+8061.36*(diff(w(r, z), z))(r, 12)+1651.12*(u(r, z))(r, 12)/r(r, 12) = 0, w(r, 0) = 0}

(1)

``

NULL

sys3 := [(L+2*m)*(diff(u(r, z), r, r))+(L+m)*(diff(w(r, z), r, z))+(L+2*m)*(diff(u(r, z), r))/r-(L+2*m)*u(r, z)/r^2+m*(diff(u(r, z), z, z)) = 0, (L+m)*(diff(u(r, z), r, z))+m*(diff(w(r, z), r, r))+(L+2*m)*(diff(w(r, z), z, z))+(L+m)*(diff(u(r, z), z))/r+m*(diff(w(r, z), r))/r = 0]

pdsolve(sys3, BCS, numeric)

 

 

``

``


Download PDE_equation2.mw

Hi all,

I have the following PDE, is it solveable by Maple or not. Do I need a boundary condition and how many or I can get a general solution? I am new to Maple. Any help will be appreciated.

Thank you.

 

 

 

Hello,

I am new to Maple. I am working on PDE and I wanted to try an easy example to know how to work with Maple. So, I startted with the example from the HELP, but still get error as shown below. Can someone guides me.

Thank you.

Hello all,

I am pretty new to Maple, but I am trying to understand something. I was able to find a numerical solution to a PDE in maple (with some community help, thanks guys!). I am trying to manipulate this data but am struggling with it. I thought if I could take this data to matlab it would be pretty easy for me to manipulate and do what I want. 

So my question is: How do I export my numerical solution (pds module) to matlab. Just taking the data is okay. I know you can evaluate the data at some points. 

 

I see there is "Matlab" command that converts code, it doesn't seem to like pds as an input though.

I also see an export matrix command. I guess it could be possible to create a matrix of plot data and convert it this way?

 

I had to do a change of coordinate system to solve the PDE because of boundary conditions. I'm trying to transform this data back to my regular x,y coordinate system to see if it matches some other simulations. 

Thanks in advance! And here is my file.


restart;
with(Physics):
Setup(mathematicalnotation = true):

V(Z, f);

If function ( varphi) is defined, use this one.

PDE1 := subs[inplace](x = xi*varphi(t), PDE1);
If function ( varphi) is defined, use this one.


PDE1 := subs[inplace](t = 2*vartheta*(1/omega), PDE1);


 

 

 

 

 

 

Thesis_Pde2_attempt.mw

I have the following code:

restart;
PDE := diff(u(x, t), t) = diff(u(x, t), x, x)-sin(x+t)+cos(x+t);
IBC:= D[1](u)(0,t)=-sin(t),
D[1](u)(1,t)=-(u(1, t))^4+(cos(1+t))^4-sin(1+t),
u(x,0)=cos(x);

pds := pdsolve( PDE, [IBC], numeric, time = t, range = 0 .. 1,

spacestep = 0.1e-1, timestep = 0.1e-1,
errorest=true
)

 

And I want to plot the difference |pds(t,x) - cos(x+t)| in maple for x=1 and t=0..5

 

I thought to use the following piece of commands but I get an error:

P:=unapply(pds, t,x);
Q:=abs(P(t,x)-cos(x+t));
Q:-plot(x=1, t=0..1);

I get an error that Q isn't a module.

I thought that unapply is used for this case, can you help me with this simple task?

 

Thanks in advance.

 

PLEASE..!! CAN ANYONE HELP ME IN CODING ON MAPPLE 13 TO CHANGE PDE INTO ODE??

MY FUNCTION IS THIS

U[t, t]-U[t, t, x, x]-(aU[]-b*U[]^3)[x, x] = 0

HAM for convective boundary layer flows? please share

can  we share code or exchange code?

email me : faisalbasir91@gmail.com/+60182236765

 

 

I am very beginner about Maple. How to get the general solution from the follwoing equations by Maple. Please help me. Its Urgent. Please help me out.

hello everyone

can any one tell me what is this anti reduction method. In the paper of serdal palmuk,the link is given bellow

http://www.hindawi.com/journals/mpe/2009/202307/

in this paper question #4 is first solved by anti reduction method for  exact solution.

but i dont understand this method,

if anybody know this then please also tell me how to solve this,

and in the next  (6 & 7 ) examples "in the pourus media equation" they first find its particular exact solution.i also dont understand this,so please tell me

actually i know how to solve ODE to find its exact solution but  i dont know how we find exact solutions of partial differtial equations,

so please help me to solve this problem

thanks

 

I'm trying to solve a beam vibration problem. I am relatively new to Maple and trying to solve PDE's. I feel like I'm pretty close, but I don't understand what's wrong here.

This is my maple file.

Thesis_Pde2_attempt.mw

as a note, I made some simplifying assumptions. I am just using part of this equation since it is less complex. And my boundary conditions are simply supported on both ends so no displacement and no 2nd derivative at the ends.

 

Any help would be greatly appreciated!!

Dear all

I have query related to generating commutator table from given Lie algebra spanning symmetries of PDE, I have ten vectors that I need to commute with each other to constitute commutator table. I have calculated all the commutations manually using "symmetrycommutator" command.

My queries is, can I convert this operation into short loop type program which automatically calculate cummutation of vectors from 1 to 10.

The Maple file is attaches with this query for reference.

Commutator_for_Infinitesimal_Generators_for_variable_coefficient_Zakharove_Kuznetsov_Equation.mw

Hello All,

 

I am doing research for my master's thesis and I am trying to type a PDE into maple and have been struggling for about 2 weeks now. I am new to Maple but have had a lot of Matlab experience. I've seen a couple of ways to do variable changes and things but I'm still.

 

These are the substitutions I'm trying to do.

into this equation, but and some of these terms are 0 (x*d/dt are 0, P, and M_e, and q_ye).

 So it is basically a Euler-Bernoulli beam with a free vibration.

I tried to use dchange to do the substitutions but I am having trouble defining ...

 or doing both

 

 

 I see why there is an error but I don't know how to fix it.

 

I've also tried

Which is close but still doesn't look quite right. because d/dt(omega*t/2) -> omega/2

 

Any thoughts?

 

Thanks in advance

How using Maple one can obtain commutator and adjoint table for given set of infinitesimal generators spanning Lie symmetries for PDE?

pde1 := 4*x*(diff(u(x, y), x))-2.*u(x, y)-y*(diff(u(x, y), y))+diff(v(x, y), y) = 0; pde2 := 4.*x.u(x, y).(diff(u(x, y), x))+(v(x, y)-y.u(x, y)).(diff(u(x, y), y))+2.*u(x, y)^2 = diff(u(x, y), `$`(y, 2))+theta(x, y); pde3 := 8.*u(x, y).theta(x, y)+4.*x.u(x, y).(diff(theta(x, y), x))+(v(x, y)+y.u(x, y)).(diff(theta(x, y), y)) = 1/100.(diff(theta(x, y), `$`(y, 2))); bc1 := u(x, 0) = 0, v(x, 0) = 0, theta(x, 0) = 1; bc2 := u(0, y) = 0, v(0, y) = 0, theta(0, y) = 0; bc3 := u(x, 20) = 0, theta(x, 20) = 0hello dear
how can i solve this three couplde pde?please help me

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