TRANSFORMED L1-ADI AND COMPACT ADI DIFFERENCE SCHEMES FOR TWO-DIMENSIONAL TIME-FRACTIONAL SUB-DIFFUSION EQUATIONS
Abstract
This paper proposes two novel alternating direction implicit (ADI) difference schemes for solving two-dimensional time-fractional sub-diffusion equations, taking into account the weak initial singularity of the solutions. To accurately capture the rapid evolution near the initial time, the Caputo time-fractional derivative is discretized using a transformed L1 method. Furthermore, central and compact finite difference methods are employed in spatial discretization to enhance computational efficiency. By using a discrete Grönwall inequality, the error estimates in $ H^1 $-norm of the two schemes are obtained. Numerical examples are presented to illustrate the effectiveness of the proposed schemes.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Differential Equations and Numerical Methods
Advanced Numerical Methods in Computational Mathematics
Publication details
- Journal / source
- Journal of Applied Analysis & Computation
- Volume
- 16
- Issue
- 3
- Pages
- 1490–1516
- Publication date
- 1 January 2026
- Language
- EN