Implementation of a Regularization-Based Numerical Method for Solving the First-Kind Volterra Integral Equation Using Python and Numpy.

A.O. Ryspaev; M.A. Temirov

doi:10.58649/hxrywk62

Authors

A.O. Ryspaev Institute of Computer Technologies and Artificial Intelligence, Bishkek, Kyrgyz Republic Author
M.A. Temirov Institute of Computer Technologies and Artificial Intelligence, Bishkek, Kyrgyz Republic Author

DOI:

https://doi.org/10.58649/hxrywk62

Keywords:

Volterra equation of the first kind, regularization, Python, NumPy, numerical methods, ill-posed problem, integral equations, inverse problems, computational experiment

Abstract

In this paper, the problem of solving the Volterra integral equation of the first kind, which belongs to the class of ill-posed problems, is considered. Based on the method of regularization and quadrature approximation, a stable numerical algorithm was created. A modern software implementation using the Python programming language and the NumPy library is presented, which provides efficient numerical processing and computational stability of the algorithm. The stability, computational complexity, and accuracy of the algorithm have been analyzed. The results of numerical experiments confirm the effectiveness of the proposed method in solving inverse problems of mathematical physics.

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