A Neuro-Swarming Intelligence-Based Computing for Second Order Singular Periodic Non-linear Boundary Value Problems

Abstract

In the present investigation, a novel neuro-swarming intelligence-based numerical computing solver is developed for solving second order non-linear singular periodic (NSP) boundary value problems (BVPs), i.e., NSP-BVPs, using the modeling strength of artificial neural networks (ANN) optimized with global search efficacy of particle swarm optimization (PSO) supported with the methodology of rapid local search by interior-point scheme (IPS), i.e., ANN-PSO-IPS. In order to check the proficiency, robustness, and stability of the designed ANN-PSO-IPS, two numerical problems of the NSP-BVPs have been presented for different numbers of neurons. The outcomes of the proposed ANN-PSO-IPS are compared with the available exact solutions to establish the worth of the solver in terms of accuracy and convergence, which is further endorsed through results of statistical performance metrics based on multiple implementations.

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

“…In the future, the proposed scheme ANN-GA-ASM can be applied as an accurate and efficient stochastic numerical solver for nonlinear singular models [42][43][44], computational models of fluid dynamics [45][46][47][48], fractional models [49][50][51][52], and biological models [53][54][55][56][57].…”

Design of Morlet Wavelet Neural Network for Solving a Class of Singular Pantograph Nonlinear Differential Models

“…The aim of the present study is to solve the singular pantograph differential model of second kind by designing a layer structure of feed-forward artificial neural networks using the Morlet wavelet activation function, while the optimization task is accomplished with the strength of global and local search terminologies of genetic algorithm (GA) and interiorpoint algorithm (IPA), i.e., MWNN-GAIPA. The stochastic procedures have been implemented to solve various problems like nonlinear SIR system of dengue fever [27], prey-predator models [28], infectious disease model [29], rotational dynamics of nanofluid flow over a stretching sheet with thermal radiation [30], HIV infection spread model [31], nonlinear periodic singular boundary value problems [32], forecasting of the financial market [33], nonlinear multisingular systems [34], singular third kind of differential model [35], COVID-19 dynamical SITR system [36] and heat conduction dynamics based human head system [37]. These cited inspirations motivated the authors to present the design of MWNN-GAIPA for solving a class of singular pantograph differential model.…”

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:…”