An Efficient Stochastic Numerical Computing Framework for the Nonlinear Higher Order Singular Models

Zulqurnain Sabir,Hafiz Abdul Wahab,Shumaila Javeed,Haci Mehmet Baskonus

doi:10.3390/fractalfract5040176

Abstract

The focus of the present study is to present a stochastic numerical computing framework based on Gudermannian neural networks (GNNs) together with the global and local search genetic algorithm (GA) and active-set approach (ASA), i.e., GNNs-GA-ASA. The designed computing framework GNNs-GA-ASA is tested for the higher order nonlinear singular differential model (HO-NSDM). Three different nonlinear singular variants based on the (HO-NSDM) have been solved by using the GNNs-GA-ASA and numerical solutions have been compared with the exact solutions to check the exactness of the designed scheme. The absolute errors have been performed to check the precision of the designed GNNs-GA-ASA scheme. Moreover, the aptitude of GNNs-GA-ASA is verified on precision, stability and convergence analysis, which are enhanced through efficiency, implication and dependability procedures with statistical data to solve the HO-NSDM.

Highlights

The research community has always taken keen interest in solving the singular nonlinear differential models
There are singular nonlinear models that have been solved by using the stochastic numerical techniques, and the delayed, prediction, fractional, functional and pantograph differential models have been treated with the stochastic computing methods [11,12,13]
genetic algorithm (GA) has been pragmatic in numerous applications, including heterogeneous bin packing optimization [37], emergency logistics humanitarian preparation [38], second order singular models [39,40], wellhead back pressure control system [41], the electricity consumption modeling [42], image steganography [43], collaborative filtering recommender system [44] and manufacturing systems [45]

Summary

Introduction

The research community has always taken keen interest in solving the singular nonlinear differential models. Various schemes have been presented to solve such models, which involve singularity. Few traditional schemes fail to solve the singular model, such as the Adams method, Milne predictor-corrector method, Runge–Kutta and Euler’s method, etc. Stochastic numerical heuristic/swarming techniques solve the singular models at exactly zero without approximating. There are singular nonlinear models that have been solved by using the stochastic numerical techniques, and the delayed, prediction, fractional, functional and pantograph differential models have been treated with the stochastic computing methods [11,12,13]. To mention the importance of the singular models, no one can deny their significance due to the variety of applications in fluid mechanics, relativity theory, dynamics of population evolution, pattern construction and chemical reactors [14,15,16,17]

Objectives

Results

Conclusion