A multiscale Abel kernel and application in viscoelastic problem
Abstract
We consider the variable-exponent Abel kernel and demonstrate its multiscale nature in modeling crossover dynamics from the initial quasi-exponential behavior to long-term power-law behavior. Then we apply this to an integro-differential equation which models, e.g. mechanical vibration of viscoelastic materials with changing material properties. We apply the Crank-Nicolson method and the linear interpolation quadrature to design a temporal second-order scheme, and develop a framework of exponentially weighted energy argument in error estimate to account for the non-positivity and non-monotonicity of the multiscale kernel. Numerical experiments are carried out to substantiate the theoretical findings and the crossover dynamics of the model.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Composite Material Mechanics
Advanced Numerical Analysis Techniques
Publication details
- Journal / source
- Communications in Mathematical Sciences
- Volume
- 24
- Issue
- 7
- Pages
- 2047–2067
- Publication date
- 1 January 2026
- Language
- EN