The Dirichlet problem for the axially symmetric potential equation in a cylindrical domain is discretized by means of a five-point difference approximation. The resulting difference equation is solved by point or line iterative methods. The rate of convergence of these methods is determined by the spectral radius of the underlying point or line Jacobi matrix. An asymptotic approximation for this spectral radius, valid for small mesh size, is derived.
|Journal||Indagationes Mathematicae A: Mathematical sciences|
|Publication status||Published - 1975|