A numerical procedure to solve Poisson’s equation in spherical coordinates

This paper sets out to present a numerical procedure that solves Poisson’s equation in a spherical coordinate system. To discretize this equation, integration techniques at the interfaces between different regions have been carried out allowing the calculation of both the potential and the corresponding field inside and outside a charge distribution. The Gauss-Seidel method is adopted to determine the potential in each region and the results, whenever compared with the analytical solutions found in the literature, come out very satisfactory, with errors less than 1% for distances of the order of 1 × 10⁻¹⁴ m and, for larger distances, they never reach 4%.

keywords
Charge distribution; Gauss-Seidel method; electrostatic potential; field; numerical solution