Work

A Crank-nicolson L1/pi Difference Scheme for Nonlinear Time Fractional Integro-differential Equation on Graded Meshes

Year: 2025

Type: article

Abstract: In this paper, a Crank-Nicolson $ L1 $/trapezoidal Product integration (PI) difference scheme is constructed to numerically solve a Volterra-type nonlinear integro-differential equation. Assuming the exact solution exhibits a weak singularity at $ t=0 $, the convergence order of the fully discrete scheme is $ \mathcal{O}\left(N^{-\min\{r\sigma, 2-\alpha, 2\}}+M^{-2}\right) $, and the stability is analyzed using an improved Gr$ \ddot{\text{o}} $nwall inequality in terms of the $ L^2 $-norm. Finally, the theoretical results are verified by numerical experiments.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20250119

Authors: Emadidin Gahalla Mohmed Elmahdi, Jianfei Huang

Institution: Yangzhou 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, Government of Jiangsu Province, Natural Science Foundation of Jiangsu Province

Awards: G1475552212, G2895417963