On Solutions to Several Classes of Differential-Algebraic Equations Based on Artificial Neural Networks

YANG Zhao; LAN Jun; WU Yongjun

doi:10.21656/1000-0887.390122

Volume 40 Issue 2

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YANG Zhao, LAN Jun, WU Yongjun. On Solutions to Several Classes of Differential-Algebraic Equations Based on Artificial Neural Networks[J]. Applied Mathematics and Mechanics, 2019, 40(2): 115-126. doi: 10.21656/1000-0887.390122

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On Solutions to Several Classes of Differential-Algebraic Equations Based on Artificial Neural Networks

doi: 10.21656/1000-0887.390122

¹Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, P.R.China;²Winning Health Technology Group Co., Ltd.,Shanghai 200072, P.R.China

Funds: The National Natural Science Foundation of China（11772293；11272201）

Received Date: 2018-04-18
Rev Recd Date: 2018-11-11
Publish Date: 2019-02-01

Abstract

Abstract

In nonlinear science, it is always an important subject and research focus to find the approximate analytical solutions to differential equations. The artificial neural network and the optimization method were combined to solve 2 special classes of differentialalgebraic equations (DAEs). The 1st 3 numerical examples, namely, the Hessenberg DAEs with indices 1, 2, 3, fell into a category of pure mathematical problems. Then the 2nd example related to EulerLagrange DAEs with indices 3, i.e. a pendulum without external force, arising from the background of nonholonomic mechanics. The approximate analytical solutions to the above 4 examples were obtained and compared with the exact solutions and the results from the RungeKutta method. High accuracy of the proposed method was demonstrated.
- artificial neural network,
- differential-algebraic equation,
- approximate analytical solution,
- optimization method

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References

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