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Article

Extrapolation Method for Non-Linear Weakly Singular Volterra Integral Equation with Time Delay

by 1, 1,*, 2 and 1
1
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
2
School of Mathematics, Chengdu Normal University, Chengdu 611130, China
*
Author to whom correspondence should be addressed.
This work was supported by the Program of Chengdu Normal University (CS18ZDZ02).
Academic Editors: Alicia Cordero Barbero and Maria Isabel Berenguer
Mathematics 2021, 9(16), 1856; https://doi.org/10.3390/math9161856
Received: 15 June 2021 / Revised: 26 July 2021 / Accepted: 3 August 2021 / Published: 5 August 2021
(This article belongs to the Special Issue Numerical Methods for Solving Nonlinear Equations)
This paper proposes an extrapolation method to solve a class of non-linear weakly singular kernel Volterra integral equations with vanishing delay. After the existence and uniqueness of the solution to the original equation are proved, we combine an improved trapezoidal quadrature formula with an interpolation technique to obtain an approximate equation, and then we enhance the error accuracy of the approximate solution using the Richardson extrapolation, on the basis of the asymptotic error expansion. Simultaneously, a posteriori error estimate for the method is derived. Some illustrative examples demonstrating the efficiency of the method are given. View Full-Text
Keywords: weakly singular kernel Volterra integral equation; proportional delay; improved trapezoidal quadrature formula; Richardson extrapolation; posteriori error estimate weakly singular kernel Volterra integral equation; proportional delay; improved trapezoidal quadrature formula; Richardson extrapolation; posteriori error estimate
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MDPI and ACS Style

Zhang, L.; Huang, J.; Li, H.; Wang, Y. Extrapolation Method for Non-Linear Weakly Singular Volterra Integral Equation with Time Delay. Mathematics 2021, 9, 1856. https://doi.org/10.3390/math9161856

AMA Style

Zhang L, Huang J, Li H, Wang Y. Extrapolation Method for Non-Linear Weakly Singular Volterra Integral Equation with Time Delay. Mathematics. 2021; 9(16):1856. https://doi.org/10.3390/math9161856

Chicago/Turabian Style

Zhang, Li, Jin Huang, Hu Li, and Yifei Wang. 2021. "Extrapolation Method for Non-Linear Weakly Singular Volterra Integral Equation with Time Delay" Mathematics 9, no. 16: 1856. https://doi.org/10.3390/math9161856

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