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Abstract

Wave partial differential equations are one of the most important topics that model, for example, the wave motion of ground vibrations. Hence, finding approximate solutions to such equations with high accuracy and speed faster than difficult and complex analytical solutions has become possible through the use of artificial intelligence and machine learning methods. This research has three goals. The first is to transform the problem of the initial value of the wave equation into its legal form and find its accurate solution. The second is to write a linear-regression neural network algorithm. The third result is applying this algorithm to find a numerical solution to the initial value problem under the study. The last step is to compare the solution using a table and figures for certain parameters and initial conditions values to demonstrate the efficiency of the artificial neural network method. Approximate solutions were obtained with an error amount close to zero compared to the real solution of the wave differential equation by applying the artificial neural network that represents the linear regression equation. This gives the advantage of high speed in obtaining the solution to this type of differential equation.

Keywords

Artificial neural network, Linear regression, LM training, Partial differential equation, Wave equation

Subject Area

Mathematics

Article Type

Article

First Page

1669

Last Page

1675

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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