Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model

Abstract

In this study, the design of a novel model based on nonlinear third-order Emden–Fowler delay differential (EF-DD) equations is presented along with two types using the sense of delay differential and standard form of the second-order EF equation. The singularity at ξ = 0 at single or multiple points of each type of the designed EF-DD model are discussed. The detail of shape factors and delayed points is provided for both types of the designed third-order EF-DD model. For the verification and validation of the model, two numerical examples are presented of each case and numerical results have been performed using the artificial neural network along with the hybrid of global and local capabilities. The comparison of the obtained numerical results with the exact solutions shows the perfection and correctness of the designed third-order EF-DD model.

IoT Technology Enabled Heuristic Model With Morlet Wavelet Neural Network for Numerical Treatment of Heterogeneous Mosquito Release Ecosystem

“…The motive of this work is to solve the above NMDS in the heterogeneous environment using the layer structure of Morlet wavelet (MWNN) kernel together with global and local search optimization schemes of genetic algorithm (GA) and active-set algorithm (ASA), i.e., MWNN-GA-ASA. Numerical stochastic approaches have been widely applied to solve a wide variety of applications, like delay singular functional model [94]- [95], COVID-19 dynamical model [96]- [97], singular fractional models [98]- [99], preypredator system [100], singular nonlinear higher order models [101]- [103], HIV infection system [104], multisingular differential systems [105]- [106] and dengue fever nonlinear system [107]. Based on these renowned applications, the authors are motivated to solve the NMDS with the help of the MWNN-GA-ASA.…”

Computational Intelligent Paradigms to Solve the Nonlinear SIR System for Spreading Infection and Treatment Using Levenberg–Marquardt Backpropagation

“…Stochastic approaches are efficient to solve many complex models using the swarming/evolutionary approaches such as singular higher order models [18][19][20][21], dusty plasma models [22], functional singular differential systems [23,24], biological models [25][26][27][28], fluid dynamic problems [29][30][31], singular Lane-Emden model [32,33], electric circuits [34,35], Thomas-Fermi singular model [36], singular three-point model [37] and periodic differential model [38]. The potential visualizations of the proposed LMB neural network are provided as:…”

An Efficient Computational Numerical Approach For Nonlinear Mathematical Influenza Disease Modelling

“…The comparison is performed based on the reference dataset of Adams results using the LMB-NN scheme. Artificial neural networks have been extensively applied in most advance and recent applications of biological system model [15][16][17][18][19], doubly singular multi-fractional order Lane-Emden system [20], singular Thomas-Fermi model [21], model of heat conduction in human head [22], functional differential models [23][24][25] and higher order nonlinear singular models [26][27][28][29]. The novelty of the presented work is itemized as:  A novel integrated design is presented using the intelligent computing scheme through the designed LMB-NN scheme to find the solutions of the nonlinear mathematical influenza disease model.…”