Abstract
The multi-term time fractional diffusion-wave equation is of important physical meaning and engineering application value. In order to meet the needs of fast solving multi-term time fractional diffusion-wave equation, an efficient difference algorithm with intrinsic parallelism is proposed in this paper. The alternating segment Crank–Nicolson (ASC-N) parallel difference scheme is constructed with four kinds of Saul’yev asymmetric schemes and the classical Crank–Nicolson (C–N) scheme, based on alternating segment technology. The theoretical analysis shows that the ASC-N scheme is second-order convergence in space and \(3-\alpha \) order convergence in time.The computing efficiency of the ASC-N scheme can save about 80% for C–N scheme when the number of space grids is large. The theoretical analysis and numerical experiments show that the ASC-N method is effective for solving multi-term time fractional diffusion-wave equation.
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Acknowledgements
The research was partly supported by the Subproject of Major Science and Technology Program of China (2017ZX07101001-01) and the Fundamental Research Funds of the Central Universities (2018MS168).
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Communicated by José Tenreiro Machado.
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Wu, L., Pan, Y. & Yang, X. An efficient alternating segment parallel finite difference method for multi-term time fractional diffusion-wave equation. Comp. Appl. Math. 40, 67 (2021). https://doi.org/10.1007/s40314-021-01455-0
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DOI: https://doi.org/10.1007/s40314-021-01455-0
Keywords
- Multi-term time fractional diffusion-wave equation
- Alternating segment Crank–Nicolson scheme
- Stability
- Convergence
- Parallel computation