Integrated meta-heuristics finite difference method for the dynamics of nonlinear unipolar electrohydrodynamic pump flow model

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.