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
Citation: 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

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

doi: 10.21656/1000-0887.390122
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
  • 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.
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