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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

restart;

with(DETools, diff_table);

kB := 0.138064852e-22;

R := 287.058;

T := 293;

p := 101325;

rho := 0.1e-2*p/(R*T);

vr := diff_table(v_r(r, z));

vz := diff_table(v_z(r, z));

eq_r := 0 = 0;

eq_p := (vr[z]-vz[r])*vr[] = (vr[]*(vr[r, z]-vz[r, r])+vz[]*(vr[z, z]-vz[z, r]))*r;

eq_z := 0 = 0;

eq_m := r*vr[r]+r*vz[z]+vr[] = 0;

pde := {eq_m, eq_p};

IBC := {v_r(1, z) = 0, v_r(r, 0) = 0, v_z(1, z) = 0, v_z(r, 0) = r^2-1};

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

 

what am I doing wrong?

it's telling me: Error, (in pdsolve/numeric/par_hyp) Incorrect number of boundary conditions, expected 3, got 2
but i did just as in the example :-/

Are there any commands in maple that will help me find a suitable function that approximates the numerical solution of:



  restart;
  PDE := diff(v(x, t), t) = diff(v(x, t), x, x);
  JACOBIINTEGRAL := int(JacobiTheta3(0, exp(-Pi^2*s))*v(1, t-s)^4, s = 0 .. t);
  IBC:= D[1](v)(0,t)=0,
        D[1](v)(1,t)=-0.000065*v(1, t)^4,
        v(x,0)=1;
#
# For x=0..1, t=0..1, the solution varies only very slowly
# so I have increased the timestep/spacestep, just to speed
# up results generation for diagnostic purposes
#
  pds := pdsolve( PDE, [IBC], numeric, time = t, range = 0 .. 1,
                  spacestep = 0.1e-1, timestep = 0.1e-1,
                  errorest=true
                )

diff(v(x, t), t) = diff(diff(v(x, t), x), x)

 

int(JacobiTheta3(0, exp(-Pi^2*s))*v(1, t-s)^4, s = 0 .. t)

 

(D[1](v))(0, t) = 0, (D[1](v))(1, t) = -0.65e-4*v(1, t)^4, v(x, 0) = 1

 

_m649569600

(1)

#
# Plot the solution over the ranges x=0..1,
# time=0..1. Not a lot happens!
#
  pds:-plot(x=1, t=0..1);

 

#
# Plot the estimated error over the ranges x=0..1,
# time=0..1
#
  pds:-plot( err(v(x,t)), x=1,t=0..1);

 

#
# Get some numerical solution values
#
  pVal:=pds:-value(v(x,t), output=procedurelist):
  for k from 0 by 0.1 to 1 do
      pVal(1, k)[2], pVal(1, k)[3];
  od;

 

t = 0., v(x, t) = Float(undefined)

 

t = .1, v(x, t) = .999977377613528229

 

t = .2, v(x, t) = .999967577518313666

 

t = .3, v(x, t) = .999959874331053822

 

t = .4, v(x, t) = .999952927885405241

 

t = .5, v(x, t) = .999946262964885979

 

t = .6, v(x, t) = .999939702966688881

 

t = .7, v(x, t) = .999933182128311282

 

t = .8, v(x, t) = .999926675964661227

 

t = .9, v(x, t) = .999920175361791563

 

t = 1.0, v(x, t) = .999913676928735229

(2)

 

 

 

Download PDEprob2_(2).mw

 

I am refering to the first graph, is there a way in maple to find an explicit suitable approximating function?

I.e, I want the function to have the same first graph obviously, it seems like addition of exponent and a line function, I tried plotting exp(-t)-0.3*t, it doesn't look like it approximates it very well. Any suggestion on how to implement this task in maple?

Thanks.

 

Hello everyone.

Tell me how to solve this equation grad(div(f(x,y,z)))+K*Laplacian(f(x,y,z))=0

Here, the function f defines a vector field.

I tried so

restart

with(Physics[Vectors]):

Physics:-Vectors:-Setup(mathematicalnotation = true)

[mathematicalnotation = true]

(1)

eq := Gradient(Divergence(f(x, y, z)))+K*Laplacian(f(x, y, z)) = 0

Error, (in Physics:-Vectors:-Nabla) Physics:-Vectors:-Divergence expected a vector function, but received the scalar function: f(x, y, z)

 

``


Download eq.mw

 

Are there any examples of network solutions such as mine systems in Maple.
I wrote in the Maple system of partial differential equations describing the process of filtration combustion.
I'm a novice. I do not quite understand how to solve it.
Online a lot of "simple" examples. I need something very similar to my case.

Model03.mw

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