SOLVING LINEAR VOLTERRA INTEGRAL EQUATIONS WITH A PIECEWISE LINEAR MAXIMUM ENTROPY METHOD

Yucheng Song; Tingting Fang; Jiu Ding; Congming Jin

doi:10.1216/jie.2023.35.119

Abstract

Based on the principle of maximum entropy and piecewise linear basis functions, a numerical method for approximating a nonnegative solution of Volterra integral equations is proposed. Then a discrete form of the maximum entropy method is given to reduce the cost. The error analysis and the convergence rate are provided. Numerical experimental results are consistent with the theoretical analysis of errors and the convergence rate.

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Yucheng Song. Tingting Fang. Jiu Ding. Congming Jin. "SOLVING LINEAR VOLTERRA INTEGRAL EQUATIONS WITH A PIECEWISE LINEAR MAXIMUM ENTROPY METHOD." J. Integral Equations Applications 35 (1) 119 - 129, Spring 2023. https://doi.org/10.1216/jie.2023.35.119

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Received: 17 July 2022; Revised: 20 November 2022; Accepted: 21 November 2022; Published: Spring 2023

First available in Project Euclid: 7 June 2023

MathSciNet: MR4598873

zbMATH: 1518.45004

Digital Object Identifier: 10.1216/jie.2023.35.119

Subjects:

Primary: 45D05 , 65R20

Keywords: maximum entropy method , piecewise linear basis functions , Volterra integral equation

Abstract

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