Hi all,

I want to get the general solution of the Laplace equation with boundary conditions below:

sys[1] := [diff(A(r, theta), r, r)+(diff(A(r, theta), r))/r+(diff(A(r, theta), theta, theta))/r^2 =0, D[2](A)(r, theta0) = 0, D[2](A)(r, theta0+beta) = 0, D[1](A)(R1, theta) = 0, A(R2,theta)=f(theta)];

pdsolve(sys[1]); do not give me the solution

Thank you to help to obtain the general solution and how (the method) to obtain this solution with Maple

Hi all,

Is there any way with "pdsolve" or 'dsolve' to get the general solution of Laplace equation in polar coordinates with boundary onditions as :

restart:sys[1] := [diff(A(r, theta), r, r)+(diff(A(r, theta), r))/r+(diff(A(r, theta), theta, theta))/r^2 =0, D[2](A)(r, theta0) = 0, D[2](A)(r, theta0+beta) = 0, D[1](A)(R1, theta) = 0, A(R2,theta)=f(theta)];

pdsolve(sys[1]);

Thanks in advance

Hi,

I have this procedure:

f := proc(x) if x < 0 then x^2+1; else cos(x); end if; end proc:

When I calculate NLPSolve(f,-Pi..2*Pi); the result is good. In NLPSolve, f(Pi) or f(-Pi) are also calculated.

When I want to determine f(Pi), I have this error code:

Error, (in f) cannot determine if this expression is true or false: Pi < 0

Why ? 

I must change my procedure with adding "evalf" to get a result for f(Pi):...

Hi

It is not corect in my problem to get different parameters a, b, c, ... for fmin, fmax and the objective function.

The probleme is to minimize the objective function (fmax-fmin)/fmoy.

NLPSolve((fmax-fmin)/fmoy,t = 0 .. Pi/p/wr,a=1..5,b=0.1..0.5,c=0.4..0.8,d=10..20,wr=200..300,p=5..20);...

Hi

The example below is the same as my code:

restart:with(Optimization):f:=(a+2*b+c*d)*sin(wr*p*t);

fmoy := p*wr*(int(f, t = 0 .. Pi/p/wr))/Pi;

fmax:=NLPSolve(f,t = 0 .. 2,a=1..5,b=0.1..0.5,c=0.4..0.8,d=10..20,wr=200..300,p=5..20,maximize);

fmin:=NLPSolve(f,t = 0 .. 2,a=1..5,b=0.1..0.5,c=0.4..0.8,d=10..20,wr=200..300,p=5..20);

Taux:=NLPSolve((fmax-fmin)/fmoy,t = 0 .. 2,a=1..5,b=0.1..0.5,c=0.4..0.8,d=10..20,wr=200..300,p=5..20);