Solution of two-point fuzzy boundary value problems by fuzzy neural networks

Mazin Hashim Suhhiem, Basim Nasih Abood, Mohammed Hadi Lafta

Abstract


In this work, we have introduced a modified method for solving second-order fuzzy differential equations. This method based on the fully fuzzy neural network to find the numerical solution of the two-point fuzzy boundary value problems for the ordinary differential equations. The fuzzy trial solution of the two-point fuzzy boundary value problems is written based on the concepts of the fully fuzzy feed-forward neural networks which containing fuzzy adjustable parameters. In comparison with other numerical methods,  the proposed method provides numerical solutions with high accuracy.


Keywords


Two-point fuzzy boundary value problem; fully fuzzy neural network ; fuzzy trial solution; minimized error function; hyperbolic tangent activation function

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References


H. Lee, I.S. Kang. Neural Algorithms For Solving Differential Equations. Journal of Computational Physics, 91, 110-131. 1990.

A.J. Meade, A.A. Fernandes. The Numerical Solution of Linear Ordinary Differential Equations by Feed-Forward Neural Networks. Mathematical and Computer Modeling, 19(12), 1-25. 1994.

A.J. Meade, A.A. Fernandes. Solution of Nonlinear Ordinary Differential Equations by Feed-Forward Neural Networks. Mathematical and Computer Modeling, 20(9), 19-44. 1994.

I.E. Lagaris, A. Likas. Artificial Neural Networks For Solving Ordinary and Partial Differential Equations. Journal of Computational Physics, 104, 1-26. 1997.

Liu, Jammes. Solving Ordinary Differential Equations by Neural Networks. Warsaw, Poland. 1999.

Tawfiq. On Design and Training of Artificial Neural Network For Solving Differential Equations. Ph.D. Thesis, College of Education, University of Baghdad, Iraq. 2004.

A. Malek, R. Shekari. Numerical Solution For High Order Differential Equations by Using a Hybrid Neural Network Optimization Method. Applied Mathematics and Computation, 183, 260-271. 2006.

S. Pattanaik, R.K. Mishra. Application of ANN For Solution of PDE in RF Engineering. International Journal on Information Sciences and Computing, 2(1), 74-79. 2008.

M. Baymani, A. Kerayechian. Artificial Neural Networks Approach For Solving Stokes Problem, Applied Mathematics, 1, 288-292. 2010.

S. Effati, M. Pakdaman. Artificial Neural Network Approach For Solving Fuzzy Differential Equations. Information Sciences, 180, 1434-1457. 2010.

M. Mosleh, M. Otadi. Fuzzy Fredholm Integro-Differential Equations with Artificial Neural Networks. Communications in Numerical Analysis, Article ID cna-00128, 1-13. 2012.

S Ezadi, N. Parandin. Numerical Solution of Fuzzy Differential Equations Based on Semi-Taylor by Using Neural Network. Journal of Basic and Applied Scientific Research, 3(1s), 477-482. 2013.

M. Mosleh, M. Otadi. Simulation and Evaluation of Fuzzy Differential Equations by Fuzzy Neural Network. Applied Soft Computing, 12, 2817-2827. 2012.

M. Mosleh. Fuzzy Neural Network For Solving a System of Fuzzy Differential Equations . Applied Soft Computing, 13, 3597-3607. 2013.

M. Mosleh, M. Otadi. Solving the Second Order Fuzzy Differential Equations by Fuzzy Neural Network . Journal of Mathematical Extension, 8(1), 11-27. 2014.

Suhhiem. Fuzzy Artificial Neural Network For Solving Fuzzy and Non-Fuzzy Differential Equations. Ph.D. Thesis, College of Sciences, AL-Mustansiriyah University, Iraq. 2016.




DOI: http://dx.doi.org/10.23755/rm.v36i1.455

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