The choice of the optimal value of the softening length (ϵ _i ) of each particle dealing with N-body simulations has a profound impact on error values in the gravitational force calculation. A slight deviation from its exact optimal value may result in a large error in the calculation. In this paper we augment the accuracy of the existing gravitational force calculation methods by providing a new technique to calculate the individual optimal values of ϵ _i for various configurations of the Plummer density model. We have proposed an expression that relates each particle by considering the average characteristic length (λ _i ) and density (ρ _i ), unlike previous studies that considered ϵ _i as an exclusive function of ρ _i . We have performed gravitational force calculations for each and every particle from the Plummer density model using compact as well as noncompact gravitational force methods based on smoothed particle hydrodynamics. We have tested our new equation for the entire range of numerical simulations performed during the study. It is found that the errors in our force calculations are not only lower than those estimated from previous studies but also remain flat for various considerations of nearest neighboring particles (N _neigh). The adjusted expression of ϵ _λ,i in our study has less dependence on N _neigh in the Plummer sphere. Finally, based on the results obtained using the method proposed in this study, we find that it remarkably improves both the accuracy as well as the stability of the gravitational force calculation.

处理N体模拟的每个粒子的软化长度 ( ϵ _i )的最佳值的选择对重力计算中的误差值具有深远的影响。与其精确最佳值的微小偏差可能会导致计算中出现较大误差。在本文中，我们通过提供一种新技术来计算Plummer 密度模型的各种配置的ϵ _i的各个最佳值，从而提高了现有重力计算方法的准确性。我们通过考虑平均特征长度 ( λ _i ) 和密度 ( ρ _i )，不像之前的研究将ϵ _i视为ρ _i的唯一函数。我们已经使用基于平滑粒子流体动力学的紧凑和非紧凑重力方法对 Plummer 密度模型中的每个粒子进行了重力计算。我们已经针对研究期间执行的整个数值模拟范围测试了我们的新方程。发现我们的力计算中的误差不仅低于先前研究估计的误差，而且对于最近相邻粒子 ( N _neigh ) 的各种考虑也保持平坦。ϵ _{λ , i}的调整后的表达式 在我们的研究中，Plummer 球体中对N _{neigh 的}依赖性较小。最后，基于使用本研究中提出的方法获得的结果，我们发现它显着提高了重力计算的准确性和稳定性。