Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Engineering with Computers
Erschienen in: Engineering with Computers 4/2022

13.06.2021 | Original Article

Computational intelligence approach using Levenberg–Marquardt backpropagation neural networks to solve the fourth-order nonlinear system of Emden–Fowler model

verfasst von: Zulqurnain Sabir, Mohamed R. Ali, Muhammad Asif Zahoor Raja, Muhammad Shoaib, Rafaél Artidoro Sandoval Núñez, R. Sadat

Erschienen in: Engineering with Computers | Sonderheft 4/2022

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The present investigations are related to design an integrated computing numerical approach through Levenberg–Marquardt backpropagation (LMB) neural networks (NNs), i.e., LMB-NNs. The designed LMB-NNs approach is presented to solve the fourth-order nonlinear system of Emden–Fowler model (FO-SEFM). The solution of six different examples based on the FO-SEFM using the designed methodology LMB-NNs is numerically treated along with the discussion of singular point and shape factor. The comparison of the obtained results from the LMB-NNs and the exact solutions of each example has been presented. To evaluate the approximate results of the FO-SEFM for different problems, the testing, training, and authentication procedures are accompanied to adapt the NNs by reducing the functions of mean square error (MSE) through the LMB. The proportional investigations and performance studies based on the results of error histograms, MSE, regression, and correlation establish the effectiveness and correctness of the designed LMB-NNs approach.
Vorheriger Artikel Thermal instability analysis of nanoscale FG porous plates embedded on Kerr foundation coupled with fluid flow
Nächster Artikel Correction to: Computational intelligence approach using Levenberg–Marquardt backpropagation neural networks to solve the fourth‑order nonlinear system of Emden–Fowler model

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Boubaker K et al (2012) Application of the BPES to Lane–Emden equations governing polytropic and isothermal gas spheres. New Astron 17(6):565–569CrossRef
2.
3.
Wazwaz AM (2005) Adomian decomposition method for a reliable treatment of the Emden–Fowler equation. Appl Math Comput 161(2):543–560MathSciNetMATH
4.
5.
Sabir Z et al (2020) Novel design of Morlet wavelet neural network for solving second order Lane-Emden equation. Math Comput Simul 172:1–14MathSciNetMATHCrossRef
6.
Adel W, et al (2020) Solving a new design of nonlinear second-order Lane–Emden pantograph delay differential model via Bernoulli collocation method. Eur Phys J Plus 135(6): 427
7.
Sabir Z et al (2021) Solving a novel designed second order nonlinear Lane–Emden delay differential model using the heuristic techniques. Appl Soft Comput 102:107105CrossRef
8.
Mandelzweig VB et al (2001) Quasi linearization approach to nonlinear problems in physics with application to nonlinear ODEs. Comput Phys Commun 141(2):268–281MathSciNetMATHCrossRef
9.
Flockerzi D, et al. (2011) On coupled Lane–Emden equations arising in dusty fluid models. J Phys Conf Ser 268(1): 012006 (IOP Publishing)
10.
Rach R et al (2014) Solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method. J Math Chem 52(1):255–267MathSciNetMATHCrossRef
11.
Khan JA et al (2015) Nature-inspired computing approach for solving non-linear singular Emden–Fowler problem arising in electromagnetic theory. Connect Sci 27(4):377–396CrossRef
12.
Luo T et al (2016) Nonlinear asymptotic stability of the Lane-Emden solutions for the viscous gaseous star problem with degenerate density dependent viscosities. Commun Math Phys 347(3):657–702MathSciNetMATHCrossRef
13.
Bhrawy AH, et al. (2014) An efficient collocation method for a class of boundary value problems arising in mathematical physics and geometry. In: Abstract and applied analysis, vol 2014. Hindawi Publishing Corporation.
14.
15.
16.
Dehghan M et al (2008) Solution of an integro-differential equation arising in oscillating magnetic fields using He’s homotopy perturbation method. Prog Electromagn Res 78:361–376CrossRef
17.
Radulescu V et al (2012) Combined effects in nonlinear problems arising in the study of anisotropic continuous media. Nonlinear Anal Theory Methods Appl 75(3):1524–1530MathSciNetMATHCrossRef
18.
Taghavi A et al (2013) A solution to the Lane–Emden equation in the theory of stellar structure utilizing the Tau method. Math Methods Appl Sci 36(10):1240–1247MathSciNetMATHCrossRef
19.
Sabir Z et al (2020) A neuro-swarming intelligence-based computing for second order singular periodic non-linear boundary value problems. Front Phys 8:224CrossRef
20.
Sabir Z, et al. (2021) Integrated intelligence of neuro-evolution with sequential quadratic programming for second-order Lane–Emden pantograph models. Math Comput Simul.
21.
Sabir Z et al (2021) Design of stochastic numerical solver for the solution of singular three-point second-order boundary value problems. Neural Comput Appl 33(7):2427–2443CrossRef
22.
23.
Sabir Z et al (2020) ‘Intelligence computing approach for solving second order system of Emden–Fowler model. J Intell Fuzzy Syst 38(6):7391–7406CrossRef
24.
Abdelkawy MA et al (2020) Numerical investigations of a new singular second-order nonlinear coupled functional Lane–Emden model. Open Phys 18(1):770–778CrossRef
25.
Parand K, Razzaghi M (2004) Rational Legendre approximation for solving some physical problems on semi-infinite intervals. Phys Scr 69(5):353MATHCrossRef
26.
Sabir Z et al (2021) Neuro-evolution computing for nonlinear multi-singular system of third order Emden–Fowler equation. Math Comput Simul 185:799–812MathSciNetMATHCrossRef
27.
Guirao JL, et al. (2020) Design and numerical solutions of a novel third-order nonlinear Emden–Fowler delay differential model. Math Prob Eng 2020
28.
Sabir Z et al (2020) Design of neuro-swarming-based heuristics to solve the third-order nonlinear multi-singular Emden–Fowler equation. Eur Phys J Plus 135(6):1–17
29.
Umar M, et al. (2021) Neuro-swarm intelligent computing paradigm for nonlinear HIV infection model with CD4+ T-cells. Math Comput Simulat
30.
Umar M et al (2020) A stochastic numerical computing heuristic of SIR nonlinear model based on dengue fever. Results Phys 19:103585CrossRef
31.
Umar M et al (2020) A stochastic intelligent computing with neuro-evolution heuristics for nonlinear SITR system of novel COVID-19 dynamics. Symmetry 12(10):1628CrossRef
32.
Umar M et al (2021) Integrated neuro-swarm heuristic with interior-point for nonlinear SITR model for dynamics of novel COVID-19. Alex Eng J 60(3):2811–2824CrossRef
33.
Sabir Z, et al. (2020) On a new model based on third-order nonlinear multisingular functional differential equations. Math Prob Eng 2020.
34.
Sabir Z, et al. (2020) Heuristic computing technique for numerical solutions of nonlinear fourth order Emden–Fowler equation. Math Comput Simul
35.
Sabir Z et al (2020) Integrated intelligent computing with neuro-swarming solver for multi-singular fourth-order nonlinear Emden–Fowler equation. Comput Appl Math 39(4):1–18MathSciNetMATHCrossRef
36.
Bukhari AH, et al. (2020) Design of a hybrid NAR-RBFs neural network for nonlinear dusty plasma system. Alexandria Eng J.
37.
Sabir Z et al (2020) Neuro-swarm intelligent computing to solve the second-order singular functional differential model. Eur Phys J Plus 135(6):474CrossRef
38.
Sabir Z et al (2019) Stochastic numerical approach for solving second order nonlinear singular functional differential equation. Appl Math Comput 363:124605MathSciNetMATH
39.
Umar M et al (2020) A stochastic computational intelligent solver for numerical treatment of mosquito dispersal model in a heterogeneous environment. Eur Phys J Plus 135(7):1–23CrossRef
40.
Raja MAZ et al (2018) Design of artificial neural network models optimized with sequential quadratic programming to study the dynamics of nonlinear Troesch’s problem arising in plasma physics. Neural Comput Appl 29(6):83–109CrossRef
41.
Umar M et al (2020) Stochastic numerical technique for solving HIV infection model of CD4+ T cells. Eur Phys J Plus 135(6):403CrossRef
42.
Sabir Z et al (2018) Neuro-heuristics for nonlinear singular Thomas–Fermi systems. Appl Soft Comput 65:152–169CrossRef
43.
Umar M et al (2021) Computational intelligent paradigms to solve the nonlinear SIR system for spreading infection and treatment using Levenberg–Marquardt backpropagation. Symmetry 13(4):618CrossRef
44.
Umar M et al (2019) Intelligent computing for numerical treatment of nonlinear prey–predator models. Appl Soft Comput 80:506–524CrossRef
45.
Umar M et al (2019) Unsupervised constrained neural network modeling of boundary value corneal model for eye surgery. Appl Soft Comput 85:105826CrossRef
46.
Mehmood et al (2018) Design of neuro-computing paradigms for nonlinear nanofluidic systems of MHD Jeffery-Hamel flow. J Taiwan Inst Chem Eng 91:57–85CrossRef
47.
Sanchez YG, (2020) Design of a nonlinear SITR fractal model based on the dynamics of a novel coronavirus (COVID).
48.
Sánchez G, et al. (2020) Analytical and approximate solutions of a novel nervous stomach mathematical model. Discrete Dyn Nat Soc 2020.
49.
Sabir Z, et al. (2020) Design of a novel second-order prediction differential model solved by using adams and explicit Runge–Kutta numerical methods. Math Prob Eng 2020.
50.
Sabir Z, et al. (2020) Integrated neuro‐evolution heuristic with sequential quadratic programming for second‐order prediction differential models. Numer Methods Part Differ Equ.
51.
Qureshi S, et al. (2020) On the use of Mohand integral transform for solving fractional-order classical Caputo differential equations.
52.
Qureshi S et al (2020) A new third order convergent numerical solver for continuous dynamical systems. J King Saud Univ Sci 32(2):1409–1416CrossRef
53.
Sabir Z et al (2020) FMNEICS: fractional Meyer neuro-evolution-based intelligent computing solver for doubly singular multi-fractional order Lane–Emden system. Comput Appl Math 39(4):1–18MathSciNetMATHCrossRef
54.
Alquran M et al (2021) Heart-cusp and bell-shaped-cusp optical solitons for an extended two-mode version of the complex Hirota model: application in optics. Opt Quant Electron 53(1):1–13CrossRef
55.
Sulaiman TA, et al. (2021) Dynamics of optical solitons and nonautonomous complex wave solutions to the nonlinear Schrodinger equation with variable coefficients. Nonlinear Dyn:1–10.
Metadaten
Titel
Computational intelligence approach using Levenberg–Marquardt backpropagation neural networks to solve the fourth-order nonlinear system of Emden–Fowler model
verfasst von
Zulqurnain Sabir
Mohamed R. Ali
Muhammad Asif Zahoor Raja
Muhammad Shoaib
Rafaél Artidoro Sandoval Núñez
R. Sadat
Publikationsdatum
13.06.2021
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe Sonderheft 4/2022
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-021-01427-2

Weitere Artikel der Sonderheft 4/2022

Engineering with Computers 4/2022 Zur Ausgabe

Original Article

On wave propagation of rotating viscoelastic nanobeams with temperature effects by using modified couple stress-based nonlocal Eringen’s theory

Original Article

Parameter tuning for wavelet transform-based damage index using mixture design

Original Article

A novel active learning method for profust reliability analysis based on the Kriging model

Original Article

Uncertainty quantification of ultimate compressive strength of CCFST columns using hybrid machine learning model

Original Article

Concurrent numerical implementation of vibration correlation technique for fast buckling load prediction of cylindrical shells under combined loading conditions

Correction

Correction to: Computational intelligence approach using Levenberg–Marquardt backpropagation neural networks to solve the fourth‑order nonlinear system of Emden–Fowler model

Neuer Inhalt

    Bildnachweise