On a Semianalytic Method for Solving Laplace´s Equation

The advantages of semianalytic methods for solving Laplace´s equation, compared to classical methods, have been pointed out recently. An approach of the former type is proposed here for twodimensional problems. The potential (or other physical quantities depending on the particular problem) is obtained in the form of a finite series: each term of this series corresponds physically to the potential created by a straight line with a uniform charge density. Basically the method consists of considering the required potential distribution to be created by an arrangement of such charged lines. The charge density of each line is then calculated in order to satisfy exactly the boundary conditions at a number of points equal to the number of line sources. the precision of the method depends on the number of sources and their arrangement;it can be very satisfactory with a relatively low number of sources especially in problems involving curve-shaped boundaries or some circular symmetry.