The present study aims to design stochastic intelligent computational heuristics for the numerical treatment of a nonlinear SITR system representing the dynamics of novel coronavirus disease 2019 (COVID-19). The mathematical SITR system using fractal parameters for COVID-19 dynamics is divided into four classes; that is, susceptible (S), infected (I), treatment (T), and recovered (R). The comprehensive details of each class along with the explanation of every parameter are provided, and the dynamics of novel COVID-19 are represented by calculating the solution of the mathematical SITR system using feed-forward artificial neural networks (FF-ANNs) trained with global search genetic algorithms (GAs) and speedy fine tuning by sequential quadratic programming (SQP)—that is, an FF-ANN-GASQP scheme. In the proposed FF-ANN-GASQP method, the objective function is formulated in the mean squared error sense using the approximate differential mapping of FF-ANNs for the SITR model, and learning of the networks is proficiently conducted with the integrated capabilities of GA and SQP. The correctness, stability, and potential of the proposed FF-ANN-GASQP scheme for the four different cases are established through comparative assessment study from the results of numerical computing with Adams solver for single as well as multiple autonomous trials. The results of statistical evaluations further authenticate the convergence and prospective accuracy of the FF-ANN-GASQP method.

https://www.mdpi.com/2073-8994/12/10/1628/pdf

A Stochastic Intelligent Computing with Neuro-Evolution Heuristics for Nonlinear SITR System of Novel COVID-19 Dynamics

This review features a survey of some recent developments in asymptotic techniques and new developments, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the achieved approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to over-come the shortcomings.In this review we have applied different powerful analytical methods to solve high nonlinear problems in engineering vibrations. Some patterns are given to illustrate the effectiveness and convenience of the methodologies.

http://www.scielo.br/pdf/lajss/v9n2/a03v9n2.pdf

Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review

The purpose of the current work is to solve the SIR nonlinear model based on dengue fever using a stochastic numerical computing scheme together with the artificial neural networks (ANNs) optimized by a well-known global genetic algorithm (GA) and local refinements of sequential quadratic programming (SQP), i.e., ANN-GA-SQM. The optimization of an error based merit function is performed by using the concepts of differential model along with the initial conditions to solve the SIR nonlinear model based dengue fever. The stochastic ANN-GA-SQM capability to solve the SIR nonlinear model based dengue fever is scrutinized to examine the correctness, precision, efficiency and constancy of the ANN-GA-SQM. The obtained numerical results of the SIR nonlinear model based dengue fever via ANN-GA-SQP are compared with the Adams results that authenticate the significance of the ANN-GA-SQM. Furthermore, statistical deliberations using the ‘semi interquartile range’, ‘mean absolute deviation’ and ‘Theil’s inequality coefficient’ have been implemented to authenticate the convergence and precision of the designed ANN-GA-SQM.

A stochastic numerical computing heuristic of SIR nonlinear model based on dengue fever

The blood flow with heat transportation has prominent clinical importance during the levels where the blood flow needs to be checked (surgery) and the heat transportation rate must be controlled (therapy). This work presents an analysis of the melting heat transport of blood, which consists of iron nanoparticles along free convection with cross-model and solution of the partial differential equation (PDEs) are emerged by the mathematical model. Being the importance of iron oxide nanoparticles in applications of the biomedical field due to their intrinsic properties such as colloidal stability, surface engineering capability and low toxicity, this study has been launched. Furthermore, PDEs of the problem are converted into a set of nonlinear ordinary differential equations (ODEs) by proper transformations. The solution of this system of ODEs is calculated through RK 4 method and Keller–Box scheme. Some leading points and numerical results of this study of both types of presence and absence of meting effects are tabulated.

Characteristics of melting heat transport of blood with time-dependent cross-nanofluid model using Keller–Box and BVP4C method

The present study is related to present a novel design of intelligent solvers with a neuro-swarm heuristic integrated with interior-point algorithm (IPA) for the numerical investigations of the nonlinear SITR fractal system based on the dynamics of a novel coronavirus (COVID-19). The mathematical form of the SITR system using fractal considerations defined in four groups, ‘susceptible (S)’, ‘infected (I)’, ‘treatment (T)’ and ‘recovered (R)’. The inclusive detail of each group along with the clarification to formulate the manipulative form of the SITR nonlinear model of novel COVID-19 dynamics is presented. The solution of the SITR model is presented using the artificial neural networks (ANNs) models trained with particle swarm optimization (PSO), i.e., global search scheme and prompt fine-tuning by IPA, i.e., ANN-PSOIPA. In the ANN-PSOIPA, the merit function is expressed for the impression of mean squared error applying the continuous ANNs form for the dynamics of SITR system and training of these networks are competently accompanied with the integrated competence of PSOIPA. The exactness, stability, reliability and prospective of the considered ANN-PSOIPA for four different forms is established via the comparative valuation from of Runge-Kutta numerical solutions for the single and multiple executions. The obtained outcomes through statistical assessments verify the convergence, stability and viability of proposed ANN-PSOIPA.

Integrated neuro-swarm heuristic with interior-point for nonlinear SITR model for dynamics of novel COVID-19

The present study is related to the effects of activation energy and thermophoretic diffusion on steady micropolar fluid along with Brownian motion. The activation energy and thermal conductivity of steady micropolar fluid are also discussed. The equation of motion, angular momentum, temperature, concentration, and their boundary conditions are presented for the micropolar fluid. The detail of geometry reveals the effects of several parameters on the parts of the system. The nonlinear partial differential equations are converted into nonlinear ordinary differential equations, and a famous shooting scheme is used to present the numerical solutions. The comparison of the obtained results by the shooting technique and the numerical bvp4c technique is presented. The behavior of local skin friction numbers and couple stress number is tabulated for different parameters, and some figures are plotted to present the different parameters. For uplifting the values of AE for parameter , the concentration profile is increased because of the Arrhenius function, and AE increases with the reduction of this function. The increasing values of the parameter of rotation G show the decrement in velocity because of the rotation of the particle of the fluid, so the linear motion decreases. Thermophoresis is responsible for shifting the molecules within the fluid, and due to this, an increment in boundary layer thickness is found, so by a greater value of , the concentration profile decreases and temperature profile goes down.

/pdf/the-effects-of-activation-energy-and-thermophoretic-44zfaflt4u.pdf

The Effects of Activation Energy and Thermophoretic Diffusion of Nanoparticles on Steady Micropolar Fluid along with Brownian Motion

On heated surface transport of heat bearing thermal radiation and MHD Cross flow with effects of nonuniform heat sink/source and buoyancy opposing/assisting flow

The main aim of the current study is to determine the effects of the temperature dependent viscosity and thermal conductivity on magnetohydrodynamics (MHD) flow of a non-Newtonian fluid over a nonlinear stretching sheet. The viscosity of the fluid depends on stratifications. Moreover, Powell–Eyring fluid is electrically conducted subject to a non-uniform applied magnetic field. Assume a small magnetic reynolds number and boundary layer approximation are applied in the mathematical formulation. Zero nano-particles mass flux condition to the sheet is considered. The governing model is transformed into the system of nonlinear Ordinary Differential Equation (ODE) system by using suitable transformations so-called similarity transformation. In order to calculate the solution of the problem, we use the higher order convergence method, so-called shooting method followed by Runge-Kutta Fehlberg (RK45) method. The impacts of different physical parameters on velocity, temperature and concentration profiles are analyzed and discussed. The parameters of engineering interest, i.e., skin fraction, Nusselt and Sherwood numbers are studied numerically as well. We concluded that the velocity profile decreases by increasing the values of S t , H and M. Also, we have analyzed the variation of temperature and concentration profiles for different physical parameters.

/pdf/numerical-study-for-the-effects-of-temperature-dependent-8s2j1t5em6.pdf

Numerical Study for the Effects of Temperature Dependent Viscosity Flow of Non-Newtonian Fluid with Double Stratification

In this article, a mathematical model of a blade coating analysis of the thin film of a Williamson fluid is developed when it passes through the small gap between a blade and a moving substrate. The conservation equations in light of lubrication approximation theory (LAT) are non-dimensionalized and solutions for the velocity, volumetric flow rate and pressure gradient are presented analytically using Adomian decomposition method. Results of the important engineering quantities like coating thickness, pressure distribution, stresses and the power input are obtained. Some results are shown graphically while others are given in tabulated form. It is found that material parameter is used to control flow rate, coating thickness, power input and the pressure distribution.

Blade coating analysis of a Williamson fluid

The current investigations are related to presenting the characteristics of flow at very high and low shear rates along with the melting process over the geometry of Riga plate. Carreau nanofluid is most appropriate mathematical viscosity model that can deal with low and high shear rates. Transportation of energy is discussed through melting conditions, thermal radiation and viscous dissipation. In this study, electromagnetic hydrodynamic aspect of nanofluid is discussed by using electromagnetic surface (Riga plate) and this system generates Lorentz force parallel to wall that keeps its effect on velocity of nanofluid. Partial differential equations (PDEs) are moved in ordinary differential equations and numerical approach named Keller Box and Shooting scheme are exercised to fetch the numerical solution of the system. An augmentation in Q leads to an enrichment in an external magnetic field. The velocity as well as momentum boundary layer booms by the virtue of an improvement in an external magnetic field. The viscosity of the nanofluid increases by the virtue of a magnification in β. Nanofluid becomes more radiated and absorbs more heat as a result of magnification in Nr, which escalates the heat transfer rate. 

Saira Bhatti

Papers

The Effects of Activation Energy and Thermophoretic Diffusion of Nanoparticles on Steady Micropolar Fluid along with Brownian Motion

On heated surface transport of heat bearing thermal radiation and MHD Cross flow with effects of nonuniform heat sink/source and buoyancy opposing/assisting flow

Numerical Study for the Effects of Temperature Dependent Viscosity Flow of Non-Newtonian Fluid with Double Stratification

Blade coating analysis of a Williamson fluid

Melting and entropy generation of infinite shear rate viscosity Carreau model over Riga plate with erratic thickness: a numerical Keller Box approach