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In this research paper, an innovative bio-inspired algorithm based on evolutionary cubic splines method (CSM) has been utilized to estimate the numerical results of nonlinear ordinary differential equation Painlevé-I. The computational mechanism is used to support the proposed technique CSM and optimize the obtained results with global search technique genetic algorithms (GAs) hybridized with sequential quadratic programming (SQP) for quick refinement. Painlevé-I is solved by the proposed technique CSM-GASQP. In this process, variation of splines is implemented for various scenarios. The CSM-GASQP produces an interpolated function that is continuous upto its second derivative. Also, splines proved to be stable than a single polynomial fitted to all points, and reduce wiggles between the tabulated points. This method provides a reliable and excellent procedure for adaptation of unknown coefficients of splines by searching globally exploiting the performance of GA-SQP algorithms. The convergence, exactness and accuracy of the proposed scheme are examined through the statistical analysis for the several independent runs. [ABSTRACT FROM AUTHOR]

Motivated by the significant role of nanofluid in pollution cleaning and energy recovery, we decided to explore the unsteady three-dimensional rotating flow of nanofluid driven by the movement of a flat surface with the potencies of prescribed heat distributions. The modeling of the physical model is completed with the help of Buongiorno nanofluid model. Suitable arrangement of similarity variables is implemented to transform the model equations into strongly nonlinear ordinary differential equations. Numerical inspection of the model is made by employing Keller–Box algorithm. Influences of involved parameters on the distributions of heat and mass are discussed graphically, while the potencies of influential parameters on reduced Nusselt and reduced Sherwood numbers are physically discussed through tabular arrangements. It is deduced that increasing the values of Prandtl factor and heat controlling indices diminishes the temperature and concentration distributions, whereas intensification in the amount of rotation factor enhances the temperature as well as concentration distribution. Moreover, negative trends in the amounts of reduced Nusselt and Sherwood numbers are achieved with the escalations in the values of rotation and thermophoresis factors, whereas opposite trend is achieved with the intensification in the choice of Prandtl factor. [ABSTRACT FROM AUTHOR]

This paper portrays the exploitation/exploration of artificial intelligence (AI) inspired computing to study the behavior of the multi-delay differential systems that revealed the impact of latent period and the dynamics of the a susceptible, vaccinated, exposed, infectious and recovered (SVEIR) epidemic model involving vaccination by means of the neural networks backpropagation with Levenberg–Marquardt scheme (NNs-BLMS). The reference solutions of the five classes ordinary differential equations (ODEs) model of SVEIR dynamics are calculated by applying the Adams method for variation in delay due to the time spent in preventing the infection and delay due to the duration of recovery immunity in the cured population. The designed NNs-BLMS used the created dataset arbitrarily for training, validation, as well as, testing samples to determine the estimated results of the nonlinear SVEIR epidemic model involving vaccination impact. The achieved accuracy of the designed NNs-BLMS is authenticated/proven by analyzing the fitness function based on mean square error (MSE), regression analysis, and error histogram for sundry scenarios of SVEIR epidemic system with the impact of vaccination. [ABSTRACT FROM AUTHOR]

The objective of this work is to explore the flow features and thermal radiation properties of the 2-D Magnetohydrodynamic (MHD) Carreau nanofluid model over an impenetrable stretching surface by utilizing the supervised learning strength of Levenberg–Marquardt backpropagation neural networking technique (LMBNNT). The mathematical formulation for MHD Carreau nanofluid flow model (MHDCNFM) in terms of partial differential equations (PDEs) is transformed into equivalent nonlinear ordinary differential equations (ODEs) by utilizing the similarity transformation and dimensional parameters. A reference dataset of proposed LMBNNT is made for Carreau nanofluid flow model exploiting the strength of Lobatto IIIA technique through the variations of different parameters against the velocity, temperature profile and concentration. These reference datasets are placed for validation, training and testing by LMBNNT and obtained outcomes are compared with reference results to check the accuracy of the designed methodology. The validation of the proposed solution methodology is obtained through the mean square error (MSE), error histogram error profile, regression p lot and fitness plot. MSE values' accuracy is upto 1 0 − 1 0 which establish the reliability of the LMBNNT. Moreover, due to an increase in Weissenberg number, fluid velocity decays in case of shear thinning liquid and higher values of Biot number enhance the temperature profile and improves the rate of heat transfer. Moreover, the increment in Hartman number reduces the surface drag force and large values of Prandtl number reduce the heat transfer process. These results of all these parameters are expressed in well-organized numerical and graphical forms. [ABSTRACT FROM AUTHOR]