Work

Homotopy Analysis Method and Physics-Informed Neural Networks for Solving Volterra Integral Equations with Discontinuous Kernels

Year: 2025

Type: article

Abstract: This paper addresses first- and second-kind Volterra integral equations (VIEs) with discontinuous kernels. A hybrid method combining the Homotopy Analysis Method (HAM) and Physics-Informed Neural Networks (PINNs) is developed. The convergence of the HAM is analyzed. Benchmark examples confirm that the proposed HAM-PINNs approach achieves high accuracy and robustness, demonstrating its effectiveness for complex kernel structures.

Source: Axioms

DOI: 10.3390/axioms14100726

Authors: Samad Noeiaghdam, Md Asadujjaman Miah, Sanda Micula

Institutions: Henan Academy of Sciences, Saveetha University, University of Dhaka, Babeș-Bolyai University, Academia Oamenilor de Știință din România

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

OpenAlex ID: W4414529266

FWCI: 2.233

Cites: 21

Cited by: 3

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