Author(s)

Huiyu Wang ¹

Affiliation(s)

¹ Beijing City University, Beijing, 101309, China

Corresponding Author

Huiyu Wang

ABSTRACT

This article discusses the application of a single hidden layer neural network algorithm in solving numerical ordinary differential equations. Set the approximate solution with neural network structure to meet the initial boundary value conditions of ordinary differential equations, and discretize the weights of neural networks in the original equations. The optimization problem is transformed into the training problem of the neural network in the approximate solution, so that the approximate solution is close to the real solution. The changes in the structure, weights, and thresholds of the neural network are observed through network deduction. Numerical examples based on the python language prove the algorithm's performance Effectiveness.

KEYWORDS

Deep neural network solution, Ordinary differential equation, Application study

CITE THIS PAPER

Huiyu Wang. Research on Deep Neural Network Solution of Ordinary Differential Equations and Its Application. Advances in Computer, Signals and Systems (2021) 5: 37-41. DOI: http://dx.doi.org/10.23977/acss.2021.050105

REFERENCES

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[3] Yuan Si, Bao Shihua. Ordinary Differential Equation Solver for Horizontal Vibration of Frame-supported Shear Walls with Variable Cross Sections, Floor Shear Walls and Wall Frame Structures. Engineering Mechanics, 1991, 8(003): 14-24.
[4] Fang Huiping, Ye Ming. Solving second-order homogeneous linear ordinary differential equations with variable coefficients. Journal of Chongqing Technology and Business University (Natural Science Edition), 2011, 28(1): 14-17.
[5] Bao Shihua, Yuan Si. Ordinary differential equation solver for the coupled vibration of frame-shear wall-thin-walled tube structure with variable cross-section. Computational Structural Mechanics and Its Applications, 1991.
[6] Fu Xiaolan, Tang Guangsong. On the Solving Theorems of Three New Types of High-Order Nonlinear Ordinary Differential Equations. Journal of Daxian Teachers College, 2000.
[7] Jia Hongyan. Application of Numerical Solution of Ordinary Differential Equations in Modeling. Journal of Xinxiang University (Journal of Natural Science), 2009.
[8] Zhao Ying, Yang Dan. Application of Ordinary Differential Equations to Solve Tesaki Theory and Application of Tesaki Theory. Heilongjiang Science and Technology Information, 2019, 6(011): 1-2.

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