Design of Morlet wavelet neural network for solving the higher order singular nonlinear differential equations

Abstract The aim of this study is to present the numerical solutions of the higher order singular nonlinear differential equations using an advanced intelligent computational approach by manipulating the Morlet wavelet (MW) neural networks (NNs), global approach as genetic algorithm (GA) and quick local search approach as interior-point method (IPM), i.e., GA-IPM. MWNNs is applied to discretize the higher order singular nonlinear differential equations to express the activation function using the mean square error. The performance of the designed MWNNs using the GA-IPM is observed to solve three different variants based on the higher order singular nonlinear differential model to check the significance, efficacy and consistency of the designed MWNNs using the GA-IPM. Furthermore, statistical performances are provided to check the precision, accuracy and convergence of the present approach.

[1]  Kalpana Jain,et al.  Traveling Salesman Problem Using Genetic Algorithm: A Survey , 2017 .

[2]  Raja Muhammad Asif Zahoor,et al.  Novel design of Morlet wavelet neural network for solving second order Lane-Emden equation , 2020, Math. Comput. Simul..

[3]  A. Alofi,et al.  An Efficient Collocation Method for a Class of Boundary Value Problems Arising in Mathematical Physics and Geometry , 2014 .

[4]  Dumitru Baleanu,et al.  A new stochastic computing paradigm for the dynamics of nonlinear singular heat conduction model of the human head , 2018, The European Physical Journal Plus.

[5]  A. Imran,et al.  The 3-D flow of Casson nanofluid over a stretched sheet with chemical reactions, velocity slip, thermal radiation and Brownian motion , 2020 .

[6]  Biorthogonal wavelets on the spectrum , 2020, Mathematical Methods in the Applied Sciences.

[7]  Muhammad Asif Zahoor Raja,et al.  A stochastic computational intelligent solver for numerical treatment of mosquito dispersal model in a heterogeneous environment , 2020, The European Physical Journal Plus.

[8]  Zulqurnain Sabir,et al.  Solving a new design of nonlinear second-order Lane–Emden pantograph delay differential model via Bernoulli collocation method , 2020 .

[9]  Juan Luis García Guirao,et al.  Integrated intelligent computing with neuro-swarming solver for multi-singular fourth-order nonlinear Emden–Fowler equation , 2020, Computational and Applied Mathematics.

[10]  C. Bender,et al.  A new perturbative approach to nonlinear problems , 1989 .

[11]  Abdul-Majid Wazwaz,et al.  Neuro-heuristics for nonlinear singular Thomas-Fermi systems , 2018, Appl. Soft Comput..

[12]  Raja Muhammad Asif Zahoor,et al.  Intelligent computing for numerical treatment of nonlinear prey-predator models , 2019, Appl. Soft Comput..

[13]  G. Muchatibaya,et al.  A nonstandard finite difference technique for singular Lane-Emden type equations , 2019, Engineering Computations.

[14]  A. Atangana,et al.  Dual fractional modeling of rate type fluid through non‐local differentiation , 2020, Numerical Methods for Partial Differential Equations.

[15]  Z. Xin,et al.  Nonlinear Asymptotic Stability of the Lane-Emden Solutions for the Viscous Gaseous Star Problem with Degenerate Density Dependent Viscosities , 2015, 1507.01069.

[16]  Alexander Domahidi,et al.  FORCES NLP: an efficient implementation of interior-point methods for multistage nonlinear nonconvex programs , 2020, Int. J. Control.

[17]  K. Nisar,et al.  Determining new soliton solutions for a generalized nonlinear evolution equation using an effective analytical method , 2020 .

[18]  A. Taghavi,et al.  A solution to the Lane–Emden equation in the theory of stellar structure utilizing the Tau method , 2013 .

[19]  Raja Muhammad Asif Zahoor,et al.  A Stochastic Intelligent Computing with Neuro-Evolution Heuristics for Nonlinear SITR System of Novel COVID-19 Dynamics , 2020, Symmetry.

[20]  Raja Muhammad Asif Zahoor,et al.  Numerical solution of doubly singular nonlinear systems using neural networks-based integrated intelligent computing , 2017, Neural Computing and Applications.

[21]  Zulqurnain Sabir,et al.  Design of stochastic numerical solver for the solution of singular three-point second-order boundary value problems , 2020, Neural Computing and Applications.

[22]  Zulqurnain Sabir,et al.  Design of a Novel Second-Order Prediction Differential Model Solved by Using Adams and Explicit Runge–Kutta Numerical Methods , 2020, Mathematical Problems in Engineering.

[23]  Grienggrai Rajchakit,et al.  Impulsive effects on stability and passivity analysis of memristor-based fractional-order competitive neural networks , 2020, Neurocomputing.

[24]  Iftikhar Ahmad,et al.  A novel design of Gaussian WaveNets for rotational hybrid nanofluidic flow over a stretching sheet involving thermal radiation , 2021 .

[25]  Ibrahim Venkat,et al.  A Genetic Algorithm Based Approach for Solving the Minimum Dominating Set of Queens Problem , 2017 .

[26]  M. Raja,et al.  Integrated neuro-swarm heuristic with interior-point for nonlinear SITR model for dynamics of novel COVID-19 , 2021, Alexandria Engineering Journal.

[27]  Juan Luis García Guirao,et al.  Stochastic numerical technique for solving HIV infection model of CD4+ T cells , 2020, The European Physical Journal Plus.

[28]  Dušan D. Repovš,et al.  Combined effects in nonlinear problems arising in the study ofanisotropic continuous media , 2012 .

[29]  Jordi Castro,et al.  Using interior point solvers for optimizing progressive lens models with spherical coordinates , 2019, Optimization and Engineering.

[30]  Ayaz Hussain Bukhari,et al.  A Stochastic Numerical Analysis Based on Hybrid NAR-RBFs Networks Nonlinear SITR Model for Novel COVID-19 Dynamics , 2022 .

[31]  Muhammad Saeed Aslam,et al.  Nature-inspired heuristic paradigms for parameter estimation of control autoregressive moving average systems , 2018, Neural Computing and Applications.

[32]  D. Flockerzi,et al.  On coupled Lane-Emden equations arising in dusty fluid models , 2011 .

[33]  D. Baleanu,et al.  A novel analytical technique to obtain the solitary solutions for nonlinear evolution equation of fractional order , 2020 .

[34]  A. Wazwaz,et al.  Solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method , 2013, Journal of Mathematical Chemistry.

[35]  A. Atangana,et al.  LOCAL AND NONLOCAL DIFFERENTIAL OPERATORS: A COMPARATIVE STUDY OF HEAT AND MASS TRANSFERS IN MHD OLDROYD-B FLUID WITH RAMPED WALL TEMPERATURE , 2020 .

[36]  Zulqurnain Sabir,et al.  Design of neuro-swarming-based heuristics to solve the third-order nonlinear multi-singular Emden–Fowler equation , 2020, The European Physical Journal Plus.

[37]  Poom Kumam,et al.  Design of Neural Network With Levenberg-Marquardt and Bayesian Regularization Backpropagation for Solving Pantograph Delay Differential Equations , 2020, IEEE Access.

[38]  Muhammad Asif Zahoor Raja,et al.  Intelligent computing for the dynamics of fluidic system of electrically conducting Ag/Cu nanoparticles with mixed convection for hydrogen possessions , 2020 .

[39]  Abdul-Majid Wazwaz,et al.  Nature-inspired computing approach for solving non-linear singular Emden–Fowler problem arising in electromagnetic theory , 2015, Connect. Sci..

[40]  Poom Kumam,et al.  Design of a hybrid NAR-RBFs neural network for nonlinear dusty plasma system , 2020 .

[41]  Raja Muhammad Asif Zahoor,et al.  Bio-inspired heuristics hybrid with interior-point method for active noise control systems without identification of secondary path , 2018, Frontiers of Information Technology & Electronic Engineering.

[42]  Robert A. Van Gorder,et al.  APPLICATION OF THE BPES TO LANE-EMDEN EQUATIONS GOVERNING POLYTROPIC AND ISOTHERMAL GAS SPHERES , 2012 .

[43]  Pradeep Jangir,et al.  A New Metaheuristic Optimization Algorithms for Brushless Direct Current Wheel Motor Design Problem , 2021, Computers, Materials & Continua.

[44]  Raja Muhammad Asif Zahoor,et al.  Integrated computational intelligent paradigm for nonlinear electric circuit models using neural networks, genetic algorithms and sequential quadratic programming , 2019, Neural Computing and Applications.

[45]  Raja Muhammad Asif Zahoor,et al.  Bio-inspired computational heuristics for Sisko fluid flow and heat transfer models , 2018, Appl. Soft Comput..

[46]  M. Khater,et al.  Numerical investigation for the fractional nonlinear space‐time telegraph equation via the trigonometric Quintic B‐spline scheme , 2020, Mathematical Methods in the Applied Sciences.

[47]  Muhammad Asif Zahoor Raja,et al.  Neuro-swarm intelligent computing to solve the second-order singular functional differential model , 2020 .

[48]  Muhammad Asif Zahoor Raja,et al.  A Levenberg–Marquardt Backpropagation Neural Network for the Numerical Treatment of Squeezing Flow With Heat Transfer Model , 2020, IEEE Access.

[49]  A. Atangana,et al.  MHD Oldroyd-B Fluid with Slip Condition in view of Local and Nonlocal Kernels , 2020 .

[50]  D. Baleanu,et al.  Lie analysis, conservation laws and travelling wave structures of nonlinear Bogoyavlenskii–Kadomtsev–Petviashvili equation , 2020 .

[51]  Adnène Arbi,et al.  Upshot of radiative rotating Prandtl fluid flow over a slippery surface embedded with variable species diffusivity and multiple convective boundary conditions , 2020, Heat Transfer.

[52]  Mohsen Razzaghi,et al.  Rational Legendre Approximation for Solving some Physical Problems on Semi-Infinite Intervals , 2004 .

[53]  Raja Muhammad Asif Zahoor,et al.  Heuristic computing technique for numerical solutions of nonlinear fourth order Emden-Fowler equation , 2020, Math. Comput. Simul..

[54]  Astronomy,et al.  Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs , 2001, physics/0102041.

[55]  Dumitru Baleanu,et al.  A NOVEL R/S FRACTAL ANALYSIS AND WAVELET ENTROPY CHARACTERIZATION APPROACH FOR ROBUST FORECASTING BASED ON SELF-SIMILAR TIME SERIES MODELING , 2020 .

[56]  Raja Muhammad Asif Zahoor,et al.  Bio-inspired heuristics hybrid with sequential quadratic programming and interior-point methods for reliable treatment of economic load dispatch problem , 2017, Neural Computing and Applications.

[57]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[58]  A. Atangana,et al.  Heat and mass transfer in Maxwell fluid in view of local and non-local differential operators , 2020, Journal of Thermal Analysis and Calorimetry.

[59]  Juan I. Ramos,et al.  Linearization methods in classical and quantum mechanics , 2003 .

[60]  Yolanda Guerrero Sánchez,et al.  A stochastic numerical computing heuristic of SIR nonlinear model based on dengue fever , 2020 .

[61]  Geert Lombaert,et al.  Interior-point methods for the phase-field approach to brittle and ductile fracture , 2020, ArXiv.

[62]  K. Nisar,et al.  Abundant solitary wave solutions to an extended nonlinear Schrödinger’s equation with conformable derivative using an efficient integration method , 2020 .

[63]  Jean-Christophe Pesquet,et al.  Deep unfolding of a proximal interior point method for image restoration , 2018, Inverse Problems.

[64]  Zulqurnain Sabir,et al.  FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system , 2020, Computational and Applied Mathematics.

[65]  Mehdi Dehghan,et al.  SOLUTION OF AN INTEGRO-DIFFERENTIAL EQUATION ARISING IN OSCILLATING MAGNETIC FIELDS USING HE'S HOMOTOPY PERTURBATION METHOD , 2008 .

[66]  M. Raja,et al.  Integrated neuro‐evolution heuristic with sequential quadratic programming for second‐order prediction differential models , 2020 .

[67]  Kottakkaran Sooppy Nisar,et al.  Novel multiple soliton solutions for some nonlinear PDEs via multiple Exp-function method , 2021 .

[68]  Z. Sabir,et al.  Numerical investigations to design a novel model based on the fifth order system of Emden–Fowler equations , 2020 .

[69]  Zulqurnain Sabir,et al.  On a New Model Based on Third-Order Nonlinear Multisingular Functional Differential Equations , 2020 .

[70]  M. Abdelkawy,et al.  Numerical investigations of a new singular second-order nonlinear coupled functional Lane–Emden model , 2020, Open Physics.

[71]  M. Irfan,et al.  Computational intelligence of Levenberg-Marquardt backpropagation neural networks to study the dynamics of expanding/contracting cylinder for Cross magneto-nanofluid flow model , 2021 .

[72]  E. Martínez-García,et al.  Exact analytic solution of an unsolvable class of first Lane–Emden equation for polytropic gas sphere , 2021 .

[73]  Vicenţiu D. Rădulescu,et al.  On a class of singular Gierer–Meinhardt systems arising in morphogenesis , 2007 .

[74]  W. Khan,et al.  Design of neural network based intelligent computing for neumerical treatment of unsteady 3D flow of Eyring-Powell magneto-nanofluidic model , 2020, Journal of Materials Research and Technology.

[75]  Raja Muhammad Asif Zahoor,et al.  Design of hybrid nature-inspired heuristics with application to active noise control systems , 2017, Neural Computing and Applications.

[76]  Abdul-Majid Wazwaz,et al.  A new algorithm for solving differential equations of Lane-Emden type , 2001, Appl. Math. Comput..

[77]  Muhammad Asif Zahoor Raja,et al.  Hybrid Bio-Inspired Computational Heuristic Paradigm for Integrated Load Dispatch Problems involving Stochastic Wind , 2019, Energies.

[78]  Iftikhar Ahmad,et al.  Intelligent computing with Levenberg–Marquardt artificial neural networks for nonlinear system of COVID-19 epidemic model for future generation disease control , 2020, The European Physical Journal Plus.