Work

High-order Numerical Scheme and Theoretical Analysis for Nonlinear Two-dimensional Fractional Volterra Integral Equations With Initial Value Singularity

Year: 2025

Type: article

Abstract: Various numerical methods have been proposed for solving one-dimensional weakly singular Volterra integral equations (VIEs) with smooth solutions. The main purpose of this paper is to propose and analyze a numerical method for the solution of two-dimensional nonlinear weakly singular VIEs with non-smooth solutions by involving the transformation of variables and modified Block-by-Block method. We rigorously prove that the new scheme can achieve an order of $ O(\tau_s^{3+\alpha}+\lambda_t^{3+\beta}) $ for non-smooth solutions with step size $ \tau_s,\lambda_t $ for $ 0<\alpha,\beta<1 $. Some numerical examples are conducted to support the theoretical results and demonstrate the effectiveness of the proposed method.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20240345

Authors: Ziqiang Wang, Xiao Wang, Junying Cao

Institution: Guizhou Minzu University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Guizhou Science and Technology Department, Guizhou Minzu University, Department of Education of Guizhou Province