Neural network for solving differential equations

Authors

  • Khalil M

    Faculty of Engineering, October University for Modern Sciences and Arts (MSA), Egypt

  • Said M

    Faculty of Engineering, October University for Modern Sciences and Arts (MSA), Egypt

  • Ibrahim A

    Faculty of Engineering, October University for Modern Sciences and Arts (MSA), Egypt

  • Elserwi H

    Faculty of Engineering, October University for Modern Sciences and Arts (MSA), Egypt

  • Mostafa B

    Faculty of Engineering, October University for Modern Sciences and Arts (MSA), Egypt

How to Cite

M, K. ., M, S. ., A, I. ., H, E. ., & B, M. . (2025). Neural network for solving differential equations. International Journal of Scientific World, 11(2), 1-7. https://doi.org/10.14419/j7yksy12

Received date: April 24, 2025

Accepted date: June 2, 2025

Published date: June 7, 2025

DOI:

https://doi.org/10.14419/j7yksy12

Keywords:

ANN; CNN; DNN; ODE; PDE

Abstract

Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) are fundamental to modelling a wide range of scientific ‎and engineering phenomena, including fluid dynamics, heat conduction, and biological systems. Classical numerical methods, such as the ‎finite difference method (FDM) and finite element method (FEM), often suffer from high computational costs, difficulty in handling com-‎plex boundary conditions, and limited scalability. With the advancement of artificial intelligence, artificial neural networks (ANNs) and con-‎convolutional neural networks (CNNs) have emerged as powerful tools for solving differential equations. This paper explores the application of ‎neural networks for solving ODEs and PDEs, analyzing their effectiveness, advantages, and limitations as neural networks are predicted to ‎transform computational mathematics, offering more accurate results‎.

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How to Cite

M, K. ., M, S. ., A, I. ., H, E. ., & B, M. . (2025). Neural network for solving differential equations. International Journal of Scientific World, 11(2), 1-7. https://doi.org/10.14419/j7yksy12

Received date: April 24, 2025

Accepted date: June 2, 2025

Published date: June 7, 2025