Landweber Iterative Regularization Method for Identifying the Initial Value Problem of the Rayleigh–Stokes Equation
- Resource Type
- article
- Authors
- Dun-Gang Li; Jun-Liang Fu; Fan Yang; Xiao-Xiao Li
- Source
- Fractal and Fractional, Vol 5, Iss 4, p 193 (2021)
- Subject
- Rayleigh–Stokes equation
ill-posed problem
identifying the initial value problem
Landweber iterative regularization method
Thermodynamics
QC310.15-319
Mathematics
QA1-939
Analysis
QA299.6-433
- Language
- English
- ISSN
- 2504-3110
In this paper, we study an inverse problem to identify the initial value problem of the homogeneous Rayleigh–Stokes equation for a generalized second-grade fluid with the Riemann–Liouville fractional derivative model. This problem is ill posed; that is, the solution (if it exists) does not depend continuously on the data. We use the Landweber iterative regularization method to solve the inverse problem. Based on a conditional stability result, the convergent error estimates between the exact solution and the regularization solution by using an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule are given. Some numerical experiments are performed to illustrate the effectiveness and stability of this method.