Thank you,

Yes I mean what you do, but when I add a value x to the first equation:

nn,kk:=2,2:

LinearAlgebra:-GenerateMatrix(
  {seq(ap[k]=x+add(a[n]*sin(n*theta)*f(n,k),n=1..nn),k=1..kk),
   seq(a[n]=add(ap[k]*g(n,k),k=1..kk),n=1..nn)},
  [seq(ap[k],k=1..kk),seq(a[n],n=1..nn)]);

I get a wrong answer for b [0 0 x x]

The correct answer is [x x 0 0]

Thanks

For lower value of nn and kk:

restart: nn:=2: kk:=2:eq1:=ap[k]=sum(a[n]*sin(n*theta)*f(n,k),n=1..nn); eq2:=a[n]=sum(ap[k]*g(n,k),k=1..kk);

seq(eq1,k=1..kk);

seq(eq2,n=1..nn);

x1:=Vector(kk,[ap[1],ap[2]]);

x2:=Vector(nn,[a[1],a[2]]);

X:=Vector(nn+kk,[x1,x2]);

A:=Matrix(kk+nn,kk+nn,[[-1,0,sin(theta)*f(1,1),sin(2*theta)*f(2,1)],[0,-1,sin(theta)*f(1,2),sin(2*theta)*f(2,2)],[g(1,1),g(1,2),-1,0],[g(2,1),g(2,2),0,-1]]);

b:=Vector(nn+kk);

When the equations are large and complicated and for high value of nn and kk, it is difficult to do manually this conversion to matrix form.

I want to automatise this. Is there any way ?

Thanks

@elango8 @elango8 Global optimization work well, but you should install the DirectSearch package from maple applications center

@elango8 @elango8 Global optimization work well, but you should install the DirectSearch package from maple applications center

You should give us in your question the boundary conditions:

boundarycond2

With those boundarycond2, you can know the constants

@monkeyhead 

restart: with(plots,implicitplot): eq1:=y=2*x^2-5*x+3: eq2:=y=x^3+4*x-3: solve({eq1,eq2},{x,y}); s:=allvalues(%);evalf(s); implicitplot([eq1, eq2], x=0..1, y=0..1, color=[blue, green], legend=[plot1,plot2]);

@monkeyhead 

restart: with(plots,implicitplot): eq1:=y=2*x^2-5*x+3: eq2:=y=x^3+4*x-3: solve({eq1,eq2},{x,y}); s:=allvalues(%);evalf(s); implicitplot([eq1, eq2], x=0..1, y=0..1, color=[blue, green], legend=[plot1,plot2]);

@Robert Israel 

In my answer below, I get the correct graph with classic worksheet !

@Robert Israel 

In my answer below, I get the correct graph with classic worksheet !

When I used your command in classic worksheet maple, I don't get the same figure as above

Why ?

When I used your command in classic worksheet maple, I don't get the same figure as above

Why ?

To get directelly F(2), using procedure is interesting

F := proc (a) options operator, arrow; eval(subs(x=a,-(int(p(x), x)))) end proc;

F(2);

To get directelly F(2), using procedure is interesting

F := proc (a) options operator, arrow; eval(subs(x=a,-(int(p(x), x)))) end proc;

F(2);

@hirnyk , PatrickT 1134

1) To determine _F1 and _F2 with boundary conditions:

subs(theta=theta0,diff(A(r,theta),theta));

                                                                 D(_F1)(ln(r)*I+theta0)+D(_F2)(-I*ln(r)+theta0)

subs(theta=theta0+beta,diff(A(r,theta),theta));

                                                                 D(_F1)(ln(r)*I+theta0+beta)+D(_F2)(-I*ln(r)+theta0+beta)

How to solve this system ?

I inform you that, there are two others boundary conditions:

D(A)(R1,theta)=0 and A(R2,theta)=f(R2,theta)

2) @Robert

Conformal mapping is not suitable for my pde (my study). I done many research in Schwarz-Christoffel mapping for many others annulus and polygons and I want to solve this pde with separation of variables.

Now, I'm solving Laplace and Poisson equation with cartesian coordinates and with separation of variables with the same newman and dirichlet conditions.

I think, I will be able to solve the pde above with dsolve and with the method of separation of variable after some experience in cartezian coordinates pdes.

In my question in maple, I was experimenting pdsolve capability.

If you can help for other methods in solving this pde with separation of variables (or other methods) and xith the four conditions, I woold be very grateful

Thank you for your help and time

@hirnyk , PatrickT 1134

1) To determine _F1 and _F2 with boundary conditions:

subs(theta=theta0,diff(A(r,theta),theta));

                                                                 D(_F1)(ln(r)*I+theta0)+D(_F2)(-I*ln(r)+theta0)

subs(theta=theta0+beta,diff(A(r,theta),theta));

                                                                 D(_F1)(ln(r)*I+theta0+beta)+D(_F2)(-I*ln(r)+theta0+beta)

How to solve this system ?

I inform you that, there are two others boundary conditions:

D(A)(R1,theta)=0 and A(R2,theta)=f(R2,theta)

2) @Robert

Conformal mapping is not suitable for my pde (my study). I done many research in Schwarz-Christoffel mapping for many others annulus and polygons and I want to solve this pde with separation of variables.

Now, I'm solving Laplace and Poisson equation with cartesian coordinates and with separation of variables with the same newman and dirichlet conditions.

I think, I will be able to solve the pde above with dsolve and with the method of separation of variable after some experience in cartezian coordinates pdes.

In my question in maple, I was experimenting pdsolve capability.

If you can help for other methods in solving this pde with separation of variables (or other methods) and xith the four conditions, I woold be very grateful

Thank you for your help and time