Abstract In this study, a new evolutionary optimized finite difference based computing paradigm is presented for dynamical analysis of dust density model for the ensemble of electrical charges and dust particles represented with nonlinear oscillatory system based on hybridization of Van-der Pol and Mathieu equation (VDP-ME). Strength of accurate and effective discretization ability of finite difference method (FDM) is exploited to transform VDP-ME to equivalent nonlinear system of algebraic equations. The residual error based fitness function of the transformed model is constructed by the competency of approximation theory in mean square sense. The optimization of the residual error of the system through hybrid meta-heuristic computing paradigm GA-SQP; genetic algorithm (GA) for viable global search aided with rapid fine tuning of sequential quadratic programming (SQP). The proposed GA-SQP-FDM is applied on variants of dust density model of VDP-ME by varying the rate of charged dust grain production, as well as, loss and comparison of results with state of art numerical procedure established the worth of the scheme in term of accuracy and convergence measures endorsed through statistical observations on large dataset.

中文翻译：

---

基于演化优化有限差分的非线性范德波尔马蒂厄振荡系统尘埃密度模型的数值计算设计

摘要 在这项研究中，提出了一种新的进化优化的基于有限差分的计算范式，用于基于范德波尔和马修方程（VDP）的混合的非线性振荡系统表示的电荷和尘埃粒子系综的尘埃密度模型的动力学分析。 -我）。利用有限差分法(FDM)精确有效的离散化能力，将VDP-ME变换为代数方程的等效非线性系统。变换模型的基于残差的适应度函数是通过均方意义上的近似理论的能力构建的。通过混合元启发式计算范式GA-SQP优化系统残差；用于可行全局搜索的遗传算法 (GA) 辅助序列二次规划 (SQP) 的快速微调。所提出的 GA-SQP-FDM 通过改变带电粉尘颗粒产生率，以及与最先进数值程序的结果的损失和比较，应用于 VDP-ME 粉尘密度模型的变体，确定了该方案的价值在通过对大型数据集的统计观察得到认可的准确性和收敛性措施方面。