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

Li Zhang, Jin Huang, Hu Li and Yifei Wang
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Li Zhang: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Jin Huang: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Hu Li: School of Mathematics, Chengdu Normal University, Chengdu 611130, China
Yifei Wang: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China

Mathematics, 2021, vol. 9, issue 16, 1-19

Abstract: 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.

Keywords: weakly singular kernel Volterra integral equation; proportional delay; improved trapezoidal quadrature formula; Richardson extrapolation; posteriori error estimate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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