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Stability analysis of a second-order difference scheme for the time-fractional mixed sub-diffusion and diffusion-wave equation.
- Source :
- Fractional Calculus & Applied Analysis; Feb2024, Vol. 27 Issue 1, p102-123, 22p
- Publication Year :
- 2024
-
Abstract
- This study investigates a class of initial-boundary value problems pertaining to the time-fractional mixed sub-diffusion and diffusion-wave equation (SDDWE). To facilitate the development of a numerical method and analysis, the original problem is transformed into a new integro-differential model which includes the Caputo derivatives and the Riemann-Liouville fractional integrals with orders belonging to (0, 1). By providing an a priori estimate of the exact solution, we have established the continuous dependence on the initial data and uniqueness of the solution for the problem. We propose a second-order method to approximate the fractional Riemann-Liouville integral and employ an L2-type formula to approximate the Caputo derivative. This results in a method with a temporal accuracy of second-order for approximating the considered model. The proof of the unconditional stability of the proposed difference scheme is established. Moreover, we demonstrate the proposed method's potential to construct and analyze a second-order L2-type numerical scheme for a broader class of the time-fractional mixed SDDWEs with multi-term time-fractional derivatives. Numerical results are presented to assess the accuracy of the method and validate the theoretical findings. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 13110454
- Volume :
- 27
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Fractional Calculus & Applied Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 175981496
- Full Text :
- https://doi.org/10.1007/s13540-023-00229-1