I am now getting quite bogged down. I have cut the problem down to a quadrant by symmetry. The two radii are maintained at potential 1 and 0, and the circular boundary is a no-flow boundary so that potential is normal there. I have u(r,theta)=1 at theta=0 for r>0.5, and u(r,theta)=0 at theta=pi/2. Also du/d_theta=0 for r=1, all theta, and du/d_theta=0 for r<0.5 and theta=0. I have used 3 oundary conditions on which is a piecewise 1. Thus: qbc1 := piecewise(0 < r and r <= .5, (D[2](u))(r, 0) = 0, 1 > r and r > .5, u(r, 0) = 1) qbc2 := (D[1](u))(1, theta) = 0 qbc3 := u(r, (1/2)*Pi) = 0 qbc := {qbc2, qbc3, qbc1} With pde: pde := Diff(u(r, theta), r, r)+(Diff(u(r, theta), r))/r+(Diff(u(r, theta), theta, theta))/r^2 = 0 I then try and solve: ans := pdsolve(pde, qbc, numeric) and get the error message: Error, (in pdsolve/numeric/par_hyp) Incorrect number of boundary conditions, expected 0, got 2 This puzzles me. I thought I had an elliptic equation, I thought I had given 4 (or possibly only 3) boundary conditions, and I thought it would expect 4. I am very grateful for all the suggetsions you have made on this problem. I now wonder whether pdsolve is the right bit of Maple to be using on this problem. It is Dirichlet's problem - solution of Laplace's equation subject to boundary conditions. Perhaps there is some other bit of Maple that solves this problem? Thanks again. John Brew