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Yıl 2019, Cilt: 9 Sayı: 4, 810 - 821, 01.12.2019

Öz

Kaynakça

  • Lee, H. and Kang, I. 1990. Neural algorithms for solving differential equations, Journal of Computa- tional Physics, 91, 110.
  • Malek, A. and Beidokhti, R.S. 2006. Numerical solution for high order differential equations using a hybrid neural network-optimization method, Applied Mathematics and Computation, 183, 260-271.
  • Lagaris, I. E., Likas, A. and Fotiadis, D. I. 1998. Artificial neural networks for solving ordinary and partial differential equations, IEEE Transactions on Neural Networks, 9(5), 987-1000.
  • Aarts, L. P. and Van Der Veer, P. 2008. Neural Network Method for Solving Partial Differential Equations, Neural Process. Lett., 14(3), 261-271.
  • McFall, K. S. and Mahan, J. R. 2009. Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions, IEEE Transactions On Neural Networks, 20(8).
  • Beidokhti, R. S. and Malek A. 2009. Solving initial-boundary value problems for systems of PDE using NN and optimization techniques, Journal of the Franklin Institute, 346, 898–913.
  • Tsoulos, G. I., Gavrillis, D. and Glavas, E. 2009. Solving differential equations with constructed neural networks, Neurocomputing, 72, 2385-2391.
  • Anastassi, A. A. 2014. Constructing Runge–Kutta methods with the use of artificial neural networks, Neural Computing and Applications, 25, 229-236.
  • Raja, M. A. Z., Manzar, M. A. and Raza, S. 2015. An efficient computational intelligence approach for solving fractional order Riccati equations using ANN and SQP, Applied Mathematical Modelling, 39, 3075-3093.
  • Kumar, M. and Yadav, N. 2015. Numerical Solution of Bratu’s Problem Using Multilayer, Natl. Acad. Sci. Letter, 38(5), 425–428.
  • Raja, M. A. Z., Khan J. A. and Chaudhary, N. I. 2016. Reliable numerical treatment of nonlinear singular Flierl–Petviashivili eq. for unbounded domain using ANN, GAs, and SQP, Applied Soft Computing, 38, 617-636.
  • Karaboga, D. 2005. An Idea Based On Honey Bee Swarm for Numerical Optimization, Technical Report-TR06, Erciyes University, Engineering Faculty, Computer Engineering Department.
  • Karaboga, D. and Akay, B. 2009. A comparative study of Artificial Bee Colony algorithm, Applied Mathematics and Computation, 214(1), 108-132.
  • Chun-Feng, W., Kui, L. and Pei-Ping, S. 2014. Hybrid artificial bee colony algorithm and particle swarm search for global optimization, Hindawi Publishing Corporation, Mathematical Problems in Engineering, Article ID 832949, 8 pages.
  • Korhan G¨unel graduated from Ege University as a mathematician. He received his one of the M.Sc. degrees in computer engineering from Dokuz Eylul University, and

A MODIFICATION OF ARTIFICIAL BEE COLONY ALGORITHM FOR SOLVING INITIAL VALUE PROBLEMS

Yıl 2019, Cilt: 9 Sayı: 4, 810 - 821, 01.12.2019

Öz

In this paper, some improvements have been made on Arti cial Bee Colony ABC algorithm to get numerical solutions of both linear and nonlinear di erential equations as initial value problems. The solutions are obtained by a feed-forward neural network trained by the modi ed ABC.

Kaynakça

  • Lee, H. and Kang, I. 1990. Neural algorithms for solving differential equations, Journal of Computa- tional Physics, 91, 110.
  • Malek, A. and Beidokhti, R.S. 2006. Numerical solution for high order differential equations using a hybrid neural network-optimization method, Applied Mathematics and Computation, 183, 260-271.
  • Lagaris, I. E., Likas, A. and Fotiadis, D. I. 1998. Artificial neural networks for solving ordinary and partial differential equations, IEEE Transactions on Neural Networks, 9(5), 987-1000.
  • Aarts, L. P. and Van Der Veer, P. 2008. Neural Network Method for Solving Partial Differential Equations, Neural Process. Lett., 14(3), 261-271.
  • McFall, K. S. and Mahan, J. R. 2009. Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions, IEEE Transactions On Neural Networks, 20(8).
  • Beidokhti, R. S. and Malek A. 2009. Solving initial-boundary value problems for systems of PDE using NN and optimization techniques, Journal of the Franklin Institute, 346, 898–913.
  • Tsoulos, G. I., Gavrillis, D. and Glavas, E. 2009. Solving differential equations with constructed neural networks, Neurocomputing, 72, 2385-2391.
  • Anastassi, A. A. 2014. Constructing Runge–Kutta methods with the use of artificial neural networks, Neural Computing and Applications, 25, 229-236.
  • Raja, M. A. Z., Manzar, M. A. and Raza, S. 2015. An efficient computational intelligence approach for solving fractional order Riccati equations using ANN and SQP, Applied Mathematical Modelling, 39, 3075-3093.
  • Kumar, M. and Yadav, N. 2015. Numerical Solution of Bratu’s Problem Using Multilayer, Natl. Acad. Sci. Letter, 38(5), 425–428.
  • Raja, M. A. Z., Khan J. A. and Chaudhary, N. I. 2016. Reliable numerical treatment of nonlinear singular Flierl–Petviashivili eq. for unbounded domain using ANN, GAs, and SQP, Applied Soft Computing, 38, 617-636.
  • Karaboga, D. 2005. An Idea Based On Honey Bee Swarm for Numerical Optimization, Technical Report-TR06, Erciyes University, Engineering Faculty, Computer Engineering Department.
  • Karaboga, D. and Akay, B. 2009. A comparative study of Artificial Bee Colony algorithm, Applied Mathematics and Computation, 214(1), 108-132.
  • Chun-Feng, W., Kui, L. and Pei-Ping, S. 2014. Hybrid artificial bee colony algorithm and particle swarm search for global optimization, Hindawi Publishing Corporation, Mathematical Problems in Engineering, Article ID 832949, 8 pages.
  • Korhan G¨unel graduated from Ege University as a mathematician. He received his one of the M.Sc. degrees in computer engineering from Dokuz Eylul University, and
Toplam 15 adet kaynakça vardır.

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Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

K. Günel Bu kişi benim

İ. Gör Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 9 Sayı: 4

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