Numerical exponential decay of the parabolic two-step model
Abstract
In this work, we study an implicit numerical scheme for the parabolic two-step model. First, we ensure the solvability, Lyapunov stability, and convergence of the numerical scheme. Then, we analyze the spectrum of the discrete Laplacian and use a discrete version of the energy method to obtain the explicit characterization En≤ME0e−ωtn of the numerical exponential decay of the approximate solutions. To the best of our knowledge, the numerical exponential decay characterization is established here for the first time in the literature. Finally, we perform numerical experiments that illustrate the theoretical results.
Fields of Study & Subjects
Gas Dynamics and Kinetic Theory
Spectral Theory in Mathematical Physics
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Journal of Thermal Stresses
- Publisher
- Informa UK Limited
- Volume
- 49
- Issue
- 4
- Pages
- 599–610
- Publication date
- 4 February 2026
- Language
- EN