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Evolutionary Intelligence
Erschienen in: Evolutionary Intelligence 4/2020

19.03.2020 | Research Paper

Single layer Chebyshev neural network model with regression-based weights for solving nonlinear ordinary differential equations

verfasst von: S. Chakraverty, Susmita Mall

Erschienen in: Evolutionary Intelligence | Ausgabe 4/2020

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Abstract

In this investigation, a novel single layer Functional Link Neural Network namely, Chebyshev artificial neural network (ChANN) model with regression-based weights has been developed to handle ordinary differential equations. In ChANN, the hidden layer is removed by an artificial expansion block of the input patterns by using Chebyshev polynomials. Thus the technique is more effectual than the multilayer ANN. Initial weights from the input layer to the output layer are taken by a regression-based model. Here, feed-forward structure and back-propagation algorithm of the unsupervised version have been utilized to make the error values minimal. Numerical examples and comparisons with other methods exhibit the superior behavior of this technique.
Vorheriger Artikel Motion planning for redundant robotic manipulators using a novel multi-group particle swarm optimization
Nächster Artikel An adaptive hybrid algorithm for social networks to choose groups with independent members

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Literatur
1.
Ricardo HJ (2009) A modern introduction to differential equations, 2nd edn. Elsevier, New YorkMATH
2.
Wazwaz AM (2002) Partial differential equations methods and applications. CRC Press, Boca RatonMATH
3.
Boyce WE, Diprima RC (2001) Elementary differential equations and boundary value problems. Wiley, New YorkMATH
4.
Pinsky MA (2003) Partial differential equations and boundary-value problems with applications. Waveland Press, Long Grove
5.
Pinchover Y, Rubinsteinan J (2005) Introduction to partial differential equations. Cambridge University Press, Cambridge
6.
Douglas J, Jones BF (1963) Predictor–corrector methods for nonlinear parabolic differential equations. J Ind Appl Math 11:195–204MathSciNetMATH
7.
Smith G (1978) Numerical solution of partial differential equations: finite difference methods. Oxford University Press, Oxford
8.
Wambecq A (1978) Rational Runge–Kutta methods for solving systems of ordinary differential equations. Computing 20:333–342MathSciNetMATH
9.
Patankar SV (1980) Numerical heat transfer and fluid flow. McGraw-Hill, New YorkMATH
10.
Conte SD, Boor C (1980) Elementary numerical analysis: an algorithmic approach. McGraw-Hill Press, New YorkMATH
11.
Lee H, Kang I (1990) Neural algorithms for solving differential equations. J Comput Phys 91:110–117MathSciNetMATH
12.
Jr Meade AJ, Fernandez AA (1994) The numerical solution of linear ordinary differential equations by feed forward neural networks. Math Comput Model 19:1–25
13.
Jr Meade AJ, Fernandez AA (1994) Solution of nonlinear ordinary differential equations by feed forward neural networks. Math Comput Model 20:19–44
14.
Lagaris IE, Likas A, Fotiadis DI (1998) Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans Neural Netw 9:987–1000
15.
Kumar M, Yadav N (2011) Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: a survey. Comput Math Appl 62:3796–3811MathSciNetMATH
16.
Ibraheem KI, Khalaf BM (2011) Shooting neural networks algorithm for solving boundary value problems in ODEs. Appl Appl Math 61:927–1941MathSciNetMATH
17.
Malek A, Beidokhti RS (2006) Numerical solution for high order differential equations, using a hybrid neural network-optimization method. Appl Math Comput 18:260–271MathSciNetMATH
18.
Yazdi HS, Pakdaman M, Modaghegh H (2011) Unsupervised kernel least mean square algorithm for solving ordinary differential equations. Nerocomputing 74:2062–2071
19.
Tsoulos IG, Gavrilis D, Glavas E (2009) Solving differential equations with constructed neural network. Neurocmputing 72:2385–2391
20.
Namatame A, Ueda N (1992) Pattern classification with Chebyshev neural network. Int J Neural Netw 3:23–31
21.
Patra JC (2011) Chebyshev neural network-based model for dual-junction solar cells. IEEE Trans Energy Convers 26:132–140
22.
Purwar S, Kar IN, Jha AN (2007) Online system identification of complex systems using Chebyshev neural network. Appl Soft Comput 7:364–372
23.
Patra JC, Kot AC (2002) Nonlinear dynamic system identification using Chebyshev functional link artificial neural network. IEEE Trans Syst Man Cybern Part B Cybern 32(4):505–511
24.
Yang SS, Tseng CS (1996) An orthogonal neural network for function approximation. IEEE Trans Syst Man Cybern Part B 26(5):779–785
25.
Patra JC, Juhola M, Meher PK (2008) Intelligent sensors using computationally efficient Chebyshev neural networks. IET Sci Meas Technol 2:68–75
26.
Bhat RB, Chakravety S (2004) Numerical analysis in engineering. Alpha Science Int Ltd, Oxford
27.
Chakraverty S, Singh VP, Sharma RK (2006) Regression based weight generation algorithm in neural network for estimation of frequencies of vibrating plates. J Comput Methods Appl Mech Eng 195:4194–4202MATH
28.
Chakraverty S, Singh VP, Sharma RK, Sharma GK (2009) Modelling vibration frequencies of annular plates by regression based neural Network. Appl Soft Comput 9:439–447
29.
Mall S, Chakraverty S (2013) Comparison of artificial neural network architecture in solving ordinary differential equations. Adv Artif Neural Syst 2013:1–24MATH
30.
Mall S, Chakraverty S (2013) Regression-based neural network training for the solution of ordinary differential equations. Int J Math Model Numer Optim 4:136–149MATH
31.
Chakraverty S, Mall S (2014) Regression based weight generation algorithm in neural network for solution of initial and boundary value problems. Neural Comput Appl 25:585–594
32.
Chakraverty S, Mall S (2017) Artificial neural networks for engineers and scientists: solving ordinary differential equations. Taylor and Francis, CRC Press, Boca RatonMATH
33.
Suli E, Mayers DF (2003) An introduction to numerical analysis. Cambridge University Press, CambridgeMATH
34.
Karris ST (2004) Numerical analysis: using MATLAB and spreadsheets. Orchard Publication, Noida
35.
Davis HT (1962) Introduction to nonlinear differential and integral equations. Dover publications Inc, New York
36.
Wazwaz AM (2005) Adomian decomposition method for a reliable treatment of the Emden–Fowler equation. Appl Math Comput 161:543–560MathSciNetMATH
37.
Chowdhury MSH, Hashim I (2007) Solutions of a class of singular second order initial value problems by homotopy-perturbation method. Phys Lett A 365:439–447MathSciNetMATH
38.
Ramos JI (2005) Linearization techniques for singular initial-value problems of ordinary differential equations. Appl Math Comput 16:1525–1542MathSciNet
39.
Liao SJ (2003) A new analytical algorithm of Lane–Emden type equations. Appl Math Comput 142:1–16MathSciNetMATH
40.
Dehghan M, Shakeri F (2008) Approximate solution of a differential equation arising in astrophysics using the variational iteration method. New Astron 13:53–59
41.
Govinder KS, Leach PGL (2007) Integrability analysis of the Emden–Fowler equation. J Nonlinear Math Phys 14:435–453MathSciNetMATH
42.
Singh OP, Pandey RK, Singh VK (2009) Analytical algorithm of Lane–Emden type equation arising in astrophysics using modified homotopy analysis method. Comput Phys Commun 180:1116–1124MATH
43.
Loia V, Parente D, Pedrycz W, Tomasiello S (2018) A granular functional network with delay: some dynamical properties and application to the sign prediction in social networks. Neurocomputing 321:61–71
44.
Wei X, Zuou Y, Luo Q, Huang H (2015) Functional network for nonlinear regression based on extreme learning machine. J Comput Theor Nanosci 12(10):3662–3666
45.
EI-Sebakhy EA, Asparouhov O, Abdulraheem AA, Al-Majed AA, Wu D, Latinski K, Raharja I (2012) Functional networks as a new data mining predictive paradigm to predict permeability in a carbonate reservoir. Expert Syst Appl 39(12):10359–10375
46.
Tomasiello S (2011) A functional network to predict fresh and hardened properties of self-compacting concretes. Int J Numer Methods Biomed Eng 27(6):840–847MATH
47.
Hadian-Rasanan AH, Rahmati D, Gorgin S, Parand K (2020) A single layer fractional orthogonal neural network for solving various types of Lane–Emden equation. New Astron 75:101307
48.
Piscopo ML, Spannowsky M, Waite P (2019) Solving differential equations with neural networks: applications to the calculation of cosmological phase transitions. Phys Rev D 100:1–12MathSciNet
49.
Waheeb W, Ghazali RA (2019) New genetically optimized tensor product functional link neural network: an application to the daily exchange rate forecasting. Evol Intell 12(4):593–608
50.
Jena PR, Majhi R (2018) An application of artificial neural network classifier to analyze the behavioral traits of smallholder farmers in Kenya. Evol Intell 11:1–11
Metadaten
Titel
Single layer Chebyshev neural network model with regression-based weights for solving nonlinear ordinary differential equations
verfasst von
S. Chakraverty
Susmita Mall
Publikationsdatum
19.03.2020
Verlag
Springer Berlin Heidelberg
Erschienen in
Evolutionary Intelligence / Ausgabe 4/2020
Print ISSN: 1864-5909
Elektronische ISSN: 1864-5917
DOI
https://doi.org/10.1007/s12065-020-00383-y

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