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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 terms of accuracy and convergence measures endorsed through statistical observations on large dataset.

In this study, a novel design of integrated biological inspired computational heuristics is presented for the dynamics of nonlinear unipolar electrohydrodynamic (UP-EHD) pump flow model by exploiting the competency of finite difference method (FDM) for discretization, global search viability of genetic algorithms (GAs) and local search efficiency of active-set method (ASM), i.e., FDM-GA-ASM. The FDM is incorporated to transform the differential equations of the UP-EHD pump flow model into a system of nonlinear algebraic equations. The cost function is constructed through the mean-square residual error by mimicking forward, central and backward difference schemes viable for a broader range of physical models. The optimum solution is achieved by the integration of global search with GAs and local search of ASM for speedy refinements. The designed stochastic numerical solver FDM-GA-ASM investigates the critical physical parameters, i.e., charge density, electric field and electric potential by varying electrical slip, Reynolds number and source number of the UP-EHD model. Statistical observations in terms of probability plots, histogram illustrations, boxplots for the cost function, mean absolute error, root mean squared error and Nash–Sutcliffe efficiency metrics are used to validate the efficiency of the FDM-GA-ASM scheme for the three variants of the UP-EHD model. The designed FDM-GA-ASM is a promising numerical computing solver for nonlinear differential systems in engineering and technology.