Numerical Stability and Convergence for Nonlinear Space-fractional Delayed Diffusion Equations with Mixed Boundary Conditions in Two Dimensions

Description

A Poster Presentation in the First XJTLU-UoL-XJTU Postgraduate Research Joint Conference & 2025 XJTLU Postgraduate Research Symposium, which won the Excellent Poster Presentation Award.
Here is the abstract:
Two-dimensional space-fractional diffusion equations with simple Dirichlet boundary conditions provide effective capabilities for modelling real-world applications. However, few studies have introduced a delayed term into two-dimensional problems with mixed boundary conditions for numerical schemes and investigations of quantitative properties. This motivated us to develop new stability and norm-based convergence analysis. In this study, we proposed a linear ADI θ-method with the shifted Grunwald-Letnikov approximation operators for Reisz-type fractional delayed Fisher equations. Under different θ, this approach induced Schur polynomials and error estimations dependent on eigenvalues of coefficient matrices to obtain the conditional stability and first-order norm convergence proof. Moreover, we extended a generalized case of Fisher equations discretised by centered difference operators with second-order accuracy. Numerical experiments were implemented to validate the theoretical results, where simulations for nonlinear Nicolson’s blowflies' equations performed better convergence. By testifying these two harmonic operators, we highlighted the interaction impacts of space-fractional derivatives in two-dimensional Fisher equations.

Period	19 Mar 2025 → 21 Mar 2025
Event title	The First XJTLU-UoL-XJTU Postgraduate Research Joint Conference & 2025 XJTLU Postgraduate Research Symposium
Event type	Conference
Location	Suzhou, ChinaShow on map
Degree of Recognition	International