Design of stochastic computational Levenberg Marquardt backpropagation-based technique to investigate temperature distribution of longitudinal moving porous fin.

The improvement of thermal exchange is of utmost interest in a wide range of engineering areas. The current study focuses on thermal evaluation involving natural radiation and convection in a fractionally arranged moving longitudinal fin model placed under a magnetic field. We implement the Levenberg Marquardt backpropagation (LMB) algorithm for investigating an innovative use of stochastic numerical computation for analyzing the efficiency of the temperature distribution in a porous moving longitudinal fin. The datasets for LMB have been created using a shooting approach for dynamic systems with varying ranges of different parameters. The validation, testing, and training processes are used to simulate networks using the LMB approach for diverse scenarios of moving porous fin models. The reliability of results is assessed based on the regression measures, absolute error, error histograms, mean square error, and other metrics for fuller numerical modeling of the suggested LMB to investigate the thermal efficiency and effectiveness of porous moving fin.

Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method.

In this study, numerical treatment of liquid crystal model described through Hunter-Saxton equation (HSE) has been presented by sinc collocation technique through theta weighted scheme due to its enormous applications including, defects, phase diagrams, self-assembly, rheology, phase transitions, interfaces, and integrated biological applications in mesophase materials and processes. Sinc functions provide the procedure for function approximation over all types of domains containing singularities, semi-infinite or infinite domains. Sinc functions have been used to reduce HSE into an algebraic system of equations that makes the solution quite superficial. These algebraic equations have been interpreted as matrices. This projected that sinc collocation technique is considerably efficacious on computational ground for higher accuracy and convergence of numerical solutions. Stability analysis of the proposed technique has ensured the accuracy and reliability of the method, moreover, as the stability parameter satisfied the condition the proposed solution of the problem converges. The solution of the HSE is presented through graphical figures and tables for different cases that are constructed on various values of θ and collocation points. The accuracy and efficiency of the proposed technique is analyzed on the basis of absolute errors.

Intelligent computing with Levenberg-Marquardt artificial neural networks for nonlinear system of COVID-19 epidemic model for future generation disease control.

The aim of this work is to design an intelligent computing paradigm through Levenberg-Marquardt artificial neural networks (LMANNs) for solving the mathematical model of Corona virus disease 19 (COVID-19) propagation via human to human interaction. The model is represented with systems of nonlinear ordinary differential equations represented with susceptible, exposed, symptomatic and infectious, super spreaders, infection but asymptomatic, hospitalized, recovery and fatality classes, and reference dataset of the COVID-19 model is generated by exploiting the strength of explicit Runge-Kutta numerical method for metropolitans of China and Pakistan including Wuhan, Karachi, Lahore, Rawalpindi and Faisalabad. The created dataset is arbitrary used for training, validation and testing processes for each cyclic update in Levenberg-Marquardt backpropagation for numerical treatment of the dynamics of COVID-19 model. The effectiveness and reliable performance of the design LMANNs are endorsed on the basis of assessments of achieved accuracy in terms of mean squared error based merit functions, error histograms and regression studies.