Volume 9 | Issue 2 | July 2024

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 Abstract

Integral equations are a class of mathematical equations that involve an unknown function under an integral sign. They are widely used to model various physical, biological, and engineering phenomena. However, solving integral equations analytically is often challenging or impossible. In this paper, we explore the use of artificial intelligence (AI) for solving integral equations. We review the existing literature on the subject and present some new results on the use of neural networks for solving Volterra integral equations. The results show that the neural network method is a promising tool for solving integral equations, and can be used to obtain accurate and efficient solutions. This paper provides a comprehensive overview of the current state of research on the use of AI for solving integral equations, and highlights the potential of this approach for solving complex mathematical problems.

 Keywords

Volterra integral equations, Artificial Intelligence, Fredholm Integral Equations, Hammerstein Integral Equations, Integral equations,Machine Learning, Deep Learning, Neural Network

 Authors and Affiliations

Dr. Hetram Suryavanshi
Assistant Professor, Department of Mathematics, Vishwavidyalaya Engineering College, Ambikapur,Chhattisgarh, India
Dr.Gopi Sao
Associate Professor & Head, Department of Mathematics, School of Engineering, Eklavya University, Damoh, Madhya Pradesh, India

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