Description
Physical processes are modelled mathematically using Partial Differential Equations(PDEs). An insight into these processes requires solving those PDEs. Since these equations most of the time do not have analytical solutions, delicate numerical methods are required. In this talk, we will explore the numerical solution of the two-dimensional quenching type nonlinear reaction-diffusion problem via dimensional splitting. The differential equation possesses a variable diffusion coefficient and a nonlinear forcing term that leads to a strong quenching singularity. Our current investigation focuses on the construction of a finite difference implementation of a Peaceman- Rachford and a Glowinski-Le Tallec splitting procedures for solving the aforementioned problem. Temporal adaptation is implemented through arc-length estimations of the rate-of- change of the numerical solution. The positivity, monotonicity and localized linear stability of the splitting schemes are analyzed.
Date of Event
Thursday November 7, 2024
Location
Parker Building 256
Preservative Splitting Numerical Schemes for Solving a Variable Coefficient Quenching Problem
Parker Building 256
Physical processes are modelled mathematically using Partial Differential Equations(PDEs). An insight into these processes requires solving those PDEs. Since these equations most of the time do not have analytical solutions, delicate numerical methods are required. In this talk, we will explore the numerical solution of the two-dimensional quenching type nonlinear reaction-diffusion problem via dimensional splitting. The differential equation possesses a variable diffusion coefficient and a nonlinear forcing term that leads to a strong quenching singularity. Our current investigation focuses on the construction of a finite difference implementation of a Peaceman- Rachford and a Glowinski-Le Tallec splitting procedures for solving the aforementioned problem. Temporal adaptation is implemented through arc-length estimations of the rate-of- change of the numerical solution. The positivity, monotonicity and localized linear stability of the splitting schemes are analyzed.
Presenter Bio
Dr. Julienne Kabre, is an assistant professor of mathematics at the Halmos College of Arts and Sciences at Nova Southeastern University, Florida, USA. She has joined the great NSU community since August 2021, where she teaches and conduct research. Prior to joining NSU, she obtained her PHD in Computational Mathematics from the Illinois Institute of Technology, Chicago, Illinois in 2017. She then completed two postdoctoral positions at the Airforce Institute of Technology in Ohio, and at Baylor University in Waco Texas. Her research interest is on numerical methods for solving partial differential equations that preserve physical properties.