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I'm trying to analytically solve for a Laplace's equation in a unit square with the following BCs: u(x,0) = 0, u(y,0) = 0, u(1,y) = 0, u(x,1) = 1

The series solution to this problem is well-known, where u(x,y) is solved with separation of variables to obtain u in terms of sin and sinh series.

I try to recreate the solution with pdsolve but am stuck with it.

My attempt:

 

lap2d := diff(u(x,y), x, x) + diff(u(x,y), y, y) = 0

sol := pdsolve(lap2d, HINT = X(x)*Y(y), build)  % saw this in mapleprimes

With this I managed to get an expression for u(x,y). My trouble is with the coefficients: _C1, _C2, _C3, _C4, _c_1

_C1 .. _C4 are clearly from integrations, but I am not clear about _c_1?

To solve for the constants of integrations, I tried to set up simultaneuous equations with the BCs.

For example,

eq1 := eval( rhs(sol), x=0) = 0

Similarly, repeat for the other 3 BCs to get eq2, eq3, eq4

I tried to solve these simultaneous eqns with:

solve({eq1, eq2, eq3, eq4}, {_C1, _C2, _C3, _C4})

but Maple does not output anyting.

Need your advice if this is the right way and I just goofed up with the syntax, or there are better ways to construct the series solution of the problem. Should I use linearsolve to find the C's?

I use Maple 17.

 

Thanks in advance

 

 

Who knows: is there a maple command for two matrix multiplication element by element without summing?

 

hi,i can not upload anything to mapleprimes.com every time i want to upload a file, i face error generating page . what should i do ?! 

Dear All,

I have problems after updating of Java to 1.7.0_55 on 14th of April. When I use the Equation Editor to write a math formula inside the Question Editing everything is going right until, after inserting renspose area, I'm going to click on the "Finish" Button. The Question Repository doesn't appear so that It's for me impossible to submit the question just written. Anyone using Maple TA has this problem?

Thank a lot for your help

giuseppe

As am trying to solve this integration:

int(B*eta^(-B)*t^(B-1)*exp(-(t/eta)^B)*(t-n*h), t = n .. (n+1)*h)

where,

ETA:=1000

B:=2.5

But this error keeps coming :

Error, (in Optimization:-NLPSolve) integration range or variable must be specified in the second argument, got 1. = 1. .. 2.

 

Please Help ..

hi all

I want to plot a 2D fig by maple. my data are in an excel file and they are too much to import them one by one manually. When I copy and paste them in maple, they appear in a column... 

thank a lot for your help.

Hi,

Maybe someone can give me a nice answer without Maple.

I am given a fourier series:
ln|cosx|=Co - sum( (-1)^k/k * cos2kx,k=1..infinity)
and am asked what this tells me about the chevychev series for ln(u).

 

Thanks

i want to plot two difrent graph in one diagram.. anyone how to do it?

restart; with(plots); n := .2; B := .5; Ec := 2.0; Pr := 1.0; N := .5; l := 1; rho := .5; c := 1; T := .5; T1 := .5; c1 := .2; c2 := .2; Gr := .5; blt := 5;

Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))^2+l*B*H(eta)*(F(eta)-(diff(f(eta), eta)))+Gr*theta(eta)-Mn*(diff(f(eta), eta)) = 0;

Eq2 := G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0;


Eq3 := G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0;

Eq4 := G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0;
                 
Eq5 := diff(theta(eta), eta, eta)+Pr*((diff(theta(eta), eta))*f(eta)-2*(diff(f(eta), eta))*theta(eta))+N*Pr*(theta1(eta)-theta(eta))/(rho*c*T)+N*Pr*Ec*(F(eta)-(diff(f(eta), eta)))^2/(rho*T1) = 0;

Eq6 := 2*F(eta)*theta1(eta)+G(eta)*(diff(theta1(eta), eta))+c1*(theta1(eta)-theta(eta))/(c*c2*T) = 0;

bcs1 := f(0) = 0, (D(f))(0) = 1, (D(f))(blt) = 0, F(blt) = 0, G(blt) = -f(blt), H(blt) = n, theta(0) = 1, theta(blt) = 0, theta1(blt) = 0;

L := [0, 1, 2];

for k to 3 do R := dsolve(eval({Eq1, Eq2, Eq3, Eq4, Eq5, Eq6, bcs1}, Mn = L[k]), [f(eta), F(eta), G(eta), H(eta), theta(eta), theta1(eta)], numeric, output = listprocedure); Y || k := rhs(R[3]); YP || k := rhs(R[5]); YR || k := rhs(R[6]); YQ || k := rhs(R[7]); YA || k := rhs(R[8]); YB || k := rhs(R[10]) end do;

plot([Y || (1 .. 3)], 0 .. 10, labels = [eta, (D(f))(eta)]);

 

this comands will comeout to diffrent graph in two diagram.. but i want two graph in one diagram.. any one know how to do it.. beside that.. i want to know how to insert arrow in diagram..

Hi

 I have the following ODEs

Restart:
a:=0.13:
b:=0.41:
reynolds:=1.125*10^8:
Eq1:=diff(f(x),x$3)+diff(f(x),x$2)*f(x)+b^2*sqrt(2*reynolds)*diff(diff(f(x),x$2)*f(x)*x^2,x$1);
Eq2:=diff(g(x),x$3)+diff(g(x),x$2)*g(x)+c*a^2*sqrt(2*reynolds)*diff(diff(g(x),x$2)*x,x$1);
f(0)=0;
D(f(0)):=0;
# continuity condition  
g(0.1*c)=f(0.1*c):
D(g(0.1*c))=D(f(0.1*c)):
(D@2)(g(0.1*c))=(D@2)(f(0.1*c)):

the value of c is unknown which must be obtained via D(g(c)):=1;

 How can I solve it?

Thanks for your attentions in advance

Amir

what is the wrong with Pi set ::: in this function ::: Warning, no iterations performed as initial point satisfies first-order conditions

Optimization[Minimize](x^2 + y^2 + 25*(sin(x)^2+sin(y)^2), x=-2*Pi .. 2*Pi , y= -2*Pi .. 2*Pi);

Warning, no iterations performed as initial point satisfies first-order conditions
[0., [x = HFloat(0.0), y = HFloat(0.0)]]


Optimization[Maximize](x^2 + y^2 + 25*(sin(x)^2+sin(y)^2), x=-2*Pi .. 2*Pi , y= -2*Pi .. 2*Pi);

Warning, no iterations performed as initial point satisfies first-order conditions
[-0., [x = HFloat(0.0), y = HFloat(0.0)]]

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

I got my good result when I apply it with this function :


f:= (x,y)->cos(x)*sin(y) -(x/(y^2+1));


Optimization[Maximize](f(x,y), x = -1 .. 2, y = -1 .. 1);


[0.994945017202501170,[x = HFloat(-0.6362676080636113), y = HFloat(1.0)]]

Optimization[Minimize](f(x,y), x = -1 .. 2, y = -1 .. 1);


[-2.02180678335978703,[x = HFloat(2.0), y = HFloat(0.10578346945175972)]]

Hi, this question is for Samir Kahn or other maplesoft staff.

Is there a way to use modelica biochem or any other chemical path library into maplesim? Do you plan to integrate this library in future versions of maplesim? Wolfram systemModeler has this library already integrated as does symbiology in matlab. Mr Kahn, I hope that your background in chemical engineering help you push for this new development in maplesim and help this product be even better than the competion. thank you and let me know as soon as possible.

juan

 

Hello,

 

Is it possible to use Maple 15 Student Edition with the same license information and purchase code both on Windows and Ubuntu?

I did a few Windows reinstalls (guess about 3) hence I used the same purchase code to activate the license that many times. Today I tried installing and using Maple 15 on Ubuntu 12.04.3 LTS 32-bit and to my dismay the license manager said, "Not enough activations left on this account." Furthermore, I have exhausted my download links and would like to know how many times Maple 15 can be activated and if the download links can be refreshed?

 

Thanks

Hi, guys and happy eastern to all! :)

I have a realy big problem. I have to do beziercurves in 3d plots.

I can´t plot it in 3d, something wrong with the plot (complex). Can anybody pls help me?! It´s very important to me, thanks! :)

im solving 4 ODe with boundary conditions.. i got this error Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 8, got 7


Hi,

I open a discussion about convolution and Fourier coefficients in Fourier series.

 

I have a function defined by f(x)=0 if x in [-Pi,0[ and 1 if x in [0,Pi[, of course f 2*Pi periodic function.

My goal is compare the Fourier coefficients of f*f ( * convolution ) and The Fourier Coefficient of f.

 

Thanks for your help.

 

 

 

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