Al-Khwarizmi
Applied Mathematics Webinar 

Next talk: Januray 06, 2026. 

Tuesday - 5:00 pm (KSA)- (2:00 p.m GMT) 

Zoom link: https://ksu-hub.zoom.us/j/97753107489

Speaker:  Manal Alotibi, King Fahd University of Petroleum & Minerals, KSA.  

Title:  Stability Analysis of Finite Difference Schemes for Wave Equations with Delay.  

Abstract: This talk presents recent advances on the stability of finite difference schemes for damped wave equations with delay effects. We consider both discrete and distributed delays within fully implicit second-order discretizations in time and space. Despite their implicit nature, these schemes do not guarantee unconditional stability due to the delayed damping terms. For the discrete delay case, stability is established using the Jury criterion applied to the associated recurrence relation. For the distributed delay case, Rouché’s Theorem provides sufficient conditions that capture the interplay between discretization parameters, damping, and the delay kernel. Quadrature techniques, including the Composite Trapezoidal Rule and Gaussian Quadrature Rule, are employed to approximate the convolution integral. Numerical experiments confirm the theoretical predictions, illustrating both stable and unstable dynamics.