AbstractThe space potential for a given boundary condition is obtained, in general, by digital simulation. In the case of an electron‐gun‐type boundary with sharp edges, confirmation of the numerical accuracy is not straightforward as singular electric field points are contained. In this paper, an accurate computation algorithm is proposed for such cases based on the Green's function method.When the computed values were compared with those by the simulation method, it was found that the present method can arrive at a high‐precision solution in a shorter period of time. In general, the analytical solution of a three‐dimensional boundary value problem containing sharp edges contain function series terms with poor convergence. Hence, the conventional acceleration method is not very effective.This paper obtains a convergence criterion suitable for the nature of the analytical solution and a significant reduction in computational time. From the nature of the basic computation equation, accuracy can be improved easily by an appropriate discretization of the numerical integral. The present method is effective for high‐precision computation of the weak electric field near the cathode. In the aberration analysis of a cathode lens, this method can be used as an effective comparison when the accuracy of the solution by the simulation is confirmed.