A Second-Order Time Discretization for Second Kind Volterra Integral Equations with Non-Smooth Solutions-Reference-Cited by-同舟云学术

A Second-Order Time Discretization for Second Kind Volterra Integral Equations with Non-Smooth Solutions

Published:2023-06-06 Issue:12 Volume:11 Page:2594
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Zhou Boya¹,Cheng Xiujun²

Affiliation:

1. School of Mathematics and Big Data, Foshan University, Foshan 528225, China

2. College of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China

Abstract

In this paper, a novel second-order method based on a change of variable and the symmetrical and repeated quadrature formula is presented for numerical solving second kind Volterra integral equations with non-smooth solutions. Applying the discrete Grönwall inequality with weak singularity, the convergence order O(N−2) in L∞ norm is proved, where N refers to the number of time steps. Numerical results are conducted to verify the efficiency and accuracy of the method.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/12/2594/pdf

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