A reproducible computational framework for green-function and Legendre-series solutions in spherical electrostatics
Description
The electrostatic potential of a point charge inside a grounded conducting sphere is a canonical boundary-value problem with an exact image-charge Green-function solution and an equivalent separated representation in Legendre polynomials. This article presents a reproducible computational framework that evaluates both representations, generates machine-readable data, regenerates publication-quality figures, and validates primary and post-processed electrostatic quantities. In response to the need for validation beyond exact-solution benchmarking, the revised framework also contains an independent cell-centred finite-volume solution of the singularity-subtracted reaction potential. It evaluates field and boundary errors, induced surface charge, image energy, physical radial force, multipole decay, computational cost, spatial error distributions, algebraic and boundary residuals, charge conservation, and inter-grid differences. The Legendre calculations improve monotonically with multipole order over the tested cases, while the independent finite-volume results display approximately second-order refinement and agree with the analytical and Legendre reaction fields. Residual and inter-grid indicators provide practical diagnostics when an exact solution is unavailable. The package is designed for computational electrostatics, spectral approximation, and verification of numerical Poisson and Laplace solvers.