A new algorithm for an iterative computation of solutions of Laplace's or Poisson's equations in two dimensions using Green's second identity is presented. This algorithm converges strongly and geometrically and can be applied to curved, irregular, or moving boundaries with nonlinear and/or discontinuous boundary conditions. It has been implemented in Pascal on a number of micro-and minicomputers and applied to several geometries. Cases with known analytic solutions have been tested. Convergence to within 0.1% to 0.01% of the theoretical values are obtained in a few minutes on a microcomputer.
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