New approximate solutions to electrostatic differential equations obtained by using numerical and analytical methods

In this paper, we implement the optimal homotopy asymptotic method to find the approximate solutions of the Poisson-Boltzmann equation. We also use the results of the conjugate gradient method for comparison with those of the optimal homotopy asymptotic method. Our study reveals that the optimal homotopy asymptotic method gives more effective results than conjugate gradient algorithms for the considered problems.