Bernoulli polynomial approximation method for solving the multi-dimensional Volterra integral equations with variable-order weakly singular kernels

Yifei Wang; Jin Huang; Hu Li

doi:10.1117/12.2685919

28 July 2023 Bernoulli polynomial approximation method for solving the multi-dimensional Volterra integral equations with variable-order weakly singular kernels

Yifei Wang, Jin Huang, Hu Li

Author Affiliations +

Proceedings Volume 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023); 127560S (2023) https://doi.org/10.1117/12.2685919
Event: 2023 3rd International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2023), 2023, Tangshan, China

Abstract

This paper proposes a method to solve (1) by approximating the unknown function with Bernoulli polynomials and then approximating the integral part with the quadrature formula. This reduces the original equation to an algebraic equation. And two numerical examples provide the absolute error to indicate the validity of the method.

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Yifei Wang, Jin Huang, and Hu Li "Bernoulli polynomial approximation method for solving the multi-dimensional Volterra integral equations with variable-order weakly singular kernels", Proc. SPIE 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023), 127560S (28 July 2023); https://doi.org/10.1117/12.2685919

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