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Stochastic Computational Approach for Complex Nonlinear Ordinary Differential Equations |
| Junaid Ali Khan1*, Muhammad Asif Zahoor Raja1**, Ijaz Mansoor Qureshi2
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1Department of Electronic Engineering, International Islamic University, Islamabad, Pakistan
2Department of Electrical Engineering, Air University, Islamabad, Pakistan
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| Cite this article: |
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Junaid Ali Khan, Muhammad Asif Zahoor Raja, Ijaz Mansoor Qureshi 2011 Chin. Phys. Lett. 28 020206 |
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Abstract We present an evolutionary computational approach for the solution of nonlinear ordinary differential equations (NLODEs). The mathematical modeling is performed by a feed-forward artificial neural network that defines an unsupervised error. The training of these networks is achieved by a hybrid intelligent algorithm, a combination of global search with genetic algorithm and local search by pattern search technique. The applicability of this approach ranges from single order NLODEs, to systems of coupled differential equations. We illustrate the method by solving a variety of model problems and present comparisons with solutions obtained by exact methods and classical numerical methods. The solution is provided on a continuous finite time interval unlike the other numerical techniques with comparable accuracy. With the advent of neuroprocessors and digital signal processors the method becomes particularly interesting due to the expected essential gains in the execution speed.
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02.60.Lj
07.05.Mh
84.35.+i
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Received: 08 November 2010
Published: 30 January 2011
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| PACS: |
02.60.Lj
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(Ordinary and partial differential equations; boundary value problems)
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07.05.Mh
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(Neural networks, fuzzy logic, artificial intelligence)
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84.35.+i
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(Neural networks)
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