  This paper is concerned with the Fourier-Bessel method for the boundary value
problems of the Helmholtz equation in a smooth simply connected domain. Based
on the denseness of Fourier-Bessel functions, the problem can be approximated
by determining the unknown coefficients in the linear combination. By the
boundary conditions, an operator equation can be obtained. We derive a lower
bound for the smallest singular value of the operator, and obtain a stability
and convergence result for the regularized solution with a suitable choice of
the regularization parameter. Numerical experiments are also presented to show
the effectiveness of the proposed method.
