Abstract
In this paper, we shall present the development of two explicit group schemes, namely, fractional explicit group (FEG) and modified fractional explicit group (MFEG) methods for solving the time fractional mobile/immobile equation in two space dimensions. The presented methods are formulated based on two Crank-Nicolson (C-N) finite difference schemes established at two different grid spacings. The stability and convergence of order O(τ2-α+ h2) are rigorously proven using Fourier analysis. Several numerical experiments are conducted to verify the efficiency of the proposed methods. Meanwhile, numerical results show that the FEG and MFEG algorithms are able to reduce the computational times and iterations effectively while preserving good accuracy in comparison to the C-N finite difference method.
| Original language | English |
|---|---|
| Article number | 188 |
| Journal | International Journal of Applied and Computational Mathematics |
| Volume | 8 |
| Issue number | 4 |
| DOIs | |
| State | Published - Aug 2022 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.
Keywords
- Convergence
- Crank-Nicolson finite difference
- Fractional mobile/immobile equation
- Grouping strategy
- Numerical experiments
- Stability
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics