Grid dependence in numerical reaction field energies and solvation forces is a well-known limitation in the finite-difference Poisson-Boltzmann methods. In this study we have investigated several numerical strategies to overcome the limitation. Specifically, we have included trimer arc dots during analytical molecular surface generation to improve the convergence of numerical reaction field energies and solvation forces. We have also utilized the level set function to trace the molecular surface implicitly to simplify the numerical mapping of the grid-independent solvent excluded surface. We have further explored to combine the weighted harmonic averaging of boundary dielectrics with a charge-based approach to improve the convergence and stability of numerical reaction field energies and solvation forces. Our test data show that the convergence and stability in both numerical energies and forces can be improved significantly when the combined strategy is applied to either the Poisson equation or the full Poisson-Boltzmann equation.