Convergence and Stability of the Split-Step θ-Milstein Method for Stochastic Delay Hopfield Neural Networks
A new splitting method designed for the numerical solutions of stochastic delay Hopfield neural networks is introduced and analysed. Under Lipschitz and linear growth conditions, this split-step θ-Milstein method is proved to have a strong convergence of order 1 in mean-square sense, which is higher...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/169214 |
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| _version_ | 1832550010769637376 |
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| author | Qian Guo Wenwen Xie Taketomo Mitsui |
| author_facet | Qian Guo Wenwen Xie Taketomo Mitsui |
| author_sort | Qian Guo |
| collection | DOAJ |
| description | A new splitting method designed for the numerical solutions of stochastic delay Hopfield neural networks is introduced and analysed. Under Lipschitz and linear growth conditions, this split-step θ-Milstein method is proved to have a strong convergence of order 1 in mean-square sense, which is higher than that of existing split-step θ-method. Further, mean-square stability of the proposed method is investigated. Numerical experiments and comparisons with existing methods illustrate the computational efficiency of our method. |
| format | Article |
| id | doaj-art-8483bd5380a0466cbd93800aebc19ff2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8483bd5380a0466cbd93800aebc19ff22025-02-03T06:07:59ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/169214169214Convergence and Stability of the Split-Step θ-Milstein Method for Stochastic Delay Hopfield Neural NetworksQian Guo0Wenwen Xie1Taketomo Mitsui2Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematical Sciences, Faculty of Science and Engineering, Doshisha University, Kyoto 610-0394, JapanA new splitting method designed for the numerical solutions of stochastic delay Hopfield neural networks is introduced and analysed. Under Lipschitz and linear growth conditions, this split-step θ-Milstein method is proved to have a strong convergence of order 1 in mean-square sense, which is higher than that of existing split-step θ-method. Further, mean-square stability of the proposed method is investigated. Numerical experiments and comparisons with existing methods illustrate the computational efficiency of our method.http://dx.doi.org/10.1155/2013/169214 |
| spellingShingle | Qian Guo Wenwen Xie Taketomo Mitsui Convergence and Stability of the Split-Step θ-Milstein Method for Stochastic Delay Hopfield Neural Networks Abstract and Applied Analysis |
| title | Convergence and Stability of the Split-Step θ-Milstein Method for Stochastic Delay Hopfield Neural Networks |
| title_full | Convergence and Stability of the Split-Step θ-Milstein Method for Stochastic Delay Hopfield Neural Networks |
| title_fullStr | Convergence and Stability of the Split-Step θ-Milstein Method for Stochastic Delay Hopfield Neural Networks |
| title_full_unstemmed | Convergence and Stability of the Split-Step θ-Milstein Method for Stochastic Delay Hopfield Neural Networks |
| title_short | Convergence and Stability of the Split-Step θ-Milstein Method for Stochastic Delay Hopfield Neural Networks |
| title_sort | convergence and stability of the split step θ milstein method for stochastic delay hopfield neural networks |
| url | http://dx.doi.org/10.1155/2013/169214 |
| work_keys_str_mv | AT qianguo convergenceandstabilityofthesplitstepthmilsteinmethodforstochasticdelayhopfieldneuralnetworks AT wenwenxie convergenceandstabilityofthesplitstepthmilsteinmethodforstochasticdelayhopfieldneuralnetworks AT taketomomitsui convergenceandstabilityofthesplitstepthmilsteinmethodforstochasticdelayhopfieldneuralnetworks |