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Year 2019, Volume 9, Issue 4, 810 - 821, 01.12.2019

Abstract

References

  • 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

Year 2019, Volume 9, Issue 4, 810 - 821, 01.12.2019

Abstract

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.

References

  • 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

Details

Primary Language English
Journal Section Research Article
Authors

K. GÜNEL This is me
Adnan Menderes University, Faculty of Arts and Sciences, Department of Mathematics, 09010, Aydın.


İ. GÖR This is me
Adnan Menderes University, Faculty of Arts and Sciences, Department of Mathematics, 09010, Aydın.

Publication Date December 1, 2019
Published in Issue Year 2019, Volume 9, Issue 4

Cite

Bibtex @ { twmsjaem760953, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2019}, volume = {9}, number = {4}, pages = {810 - 821}, title = {A MODIFICATION OF ARTIFICIAL BEE COLONY ALGORITHM FOR SOLVING INITIAL VALUE PROBLEMS}, key = {cite}, author = {Günel, K. and Gör, İ.} }