Analysis of Third-Order Nonlinear Multi-Singular Emden–Fowler Equation by Using the LeNN-WOA-NM Algorithm
TLDR
In this paper, a novel soft computing algorithm is designed for the numerical solution of third-order nonlinear multi-singular Emden-Fowler equation (TONMS-EFE) using the strength of universal approximation capabilities of Legendre polynomials based Legendre neural networks supported with optimization power of the Whale Optimization Algorithm (WOA) and Nelder-Mead (NM) algorithm.Abstract:
In this paper, a novel soft computing algorithm is designed for the numerical solution of third-order nonlinear multi-singular Emden–Fowler equation (TONMS-EFE) using the strength of universal approximation capabilities of Legendre polynomials based Legendre neural networks supported with optimization power of the Whale Optimization Algorithm (WOA) and Nelder-Mead (NM) algorithm. Unsupervised error functions are constructed in terms of mean square error for governing TONMS-EF equations of first and second order. Unknown designed parameters in LeNN structure are optimized initially by WOA for global search while NM algorithm further enhances the rapid local search convergence. The proposed algorithm’s objective is to show the accuracy and robustness in solving challenging problems like TONMS-EFE. To study our designed scheme’s performance and effectiveness, LeNN-WOA-NM is implemented on four cases of TONMS-EFE. The results obtained by the proposed algorithm are compared with the Particle Swarm Optimization (PSO) algorithm, Cuckoo search algorithm (CSA), and WOA. Extensive graphical and statistical analysis for fitness value, absolute errors, and performance indicators in terms of mean, median, and standard deviations show the proposed algorithm’s efficiency and accuracy.read more
Citations
More filters
Journal ArticleDOI
Application of Euler Neural Networks with Soft Computing Paradigm to Solve Nonlinear Problems Arising in Heat Transfer.
Naveed Ahmad Khan,Osamah Ibrahim Khalaf,Carlos Andrés Tavera Romero,Muhammad Sulaiman,Maharani Abu Bakar +4 more
TL;DR: In this article, a novel application of neurocomputing technique is presented for solving nonlinear heat transfer and natural convection porous fin problems arising in almost all areas of engineering and technology, especially in mechanical engineering.
Journal ArticleDOI
Application of Intelligent Paradigm through Neural Networks for Numerical Solution of Multiorder Fractional Differential Equations
TL;DR: The approximate solutions by the BLM-NN algorithm are compared with analytical solutions and performance based on mean square error (MSE), error histogram (EH), regression, and curve fitting further validates the accuracy, robustness, and efficiency of the proposed algorithm.
Journal ArticleDOI
Theoretical Analysis on Absorption of Carbon Dioxide (CO2) into Solutions of Phenyl Glycidyl Ether (PGE) Using Nonlinear Autoregressive Exogenous Neural Networks
TL;DR: In this article, the authors analyzed the mass transfer model with chemical reactions during the absorption of carbon dioxide (CO2) into phenyl glycidyl ether (PGE) solution.
Journal ArticleDOI
Thermal Analysis of Conductive-Convective-Radiative Heat Exchangers With Temperature Dependent Thermal Conductivity
TL;DR: In this paper, an intelligent soft computing paradigm named as the LeNN-WOA-NM algorithm is designed to analyze the mathematical model for the temperature field of convective-conductive-radiative fin with thermal conductivity depending on temperature.
Journal ArticleDOI
Mathematical models of CBSC over wireless channels and their analysis by using the LeNN-WOA-NM algorithm
TL;DR: In this paper , a novel computational paradigm that uses weighted Legendre polynomials to construct series solutions for mathematical models of the Lorenz Chaotic Attractor and Double Scroll Attractor (DSA) by using Chua's circuits was designed.
References
More filters
Journal ArticleDOI
The Whale Optimization Algorithm
Seyedali Mirjalili,Andrew Lewis +1 more
TL;DR: Optimization results prove that the WOA algorithm is very competitive compared to the state-of-art meta-heuristic algorithms as well as conventional methods.
Journal ArticleDOI
A new algorithm for solving differential equations of Lane-Emden type
TL;DR: A reliable algorithm is employed to investigate the differential equations of Lane-Emden type using the Adomian decomposition method with an alternate framework designed to overcome the difficulty of the singular point.
Journal ArticleDOI
A hybrid simplex search and particle swarm optimization for unconstrained optimization
Shu-Kai S. Fan,Erwie Zahara +1 more
TL;DR: The hybrid NM-PSO algorithm based on the Nelder–Mead (NM) simplex search method and particle swarm optimization (PSO) for unconstrained optimization is proposed to demonstrate how the standard particle swarm optimizers can be improved by incorporating a hybridization strategy.
Journal ArticleDOI
Hybrid Nelder-Mead simplex search and particle swarm optimization for constrained engineering design problems
Erwie Zahara,Yi-Tung Kao +1 more
TL;DR: This paper proposes embedding constraint handling methods, which include the gradient repair method and constraint fitness priority-based ranking method, in NM-PSO as a special operator to deal with satisfying constraints.