A high-order scheme to approximate the Caputo fractional derivative and its application to solve the fractional diffusion wave equation
| Autor: | Zongqi Liang, Yubin Yan, Ruilian Du |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Physics
Numerical Analysis Physics and Astronomy (miscellaneous) Applied Mathematics Mathematical analysis Finite difference method 010103 numerical & computational mathematics Space (mathematics) Wave equation 01 natural sciences Computer Science Applications Fractional calculus 010101 applied mathematics Computational Mathematics Modeling and Simulation Scheme (mathematics) Convergence (routing) Fractional diffusion Order (group theory) 0101 mathematics |
| Zdroj: | Journal of Computational Physics. 376:1312-1330 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2018.10.011 |
| Popis: | A new high-order finite difference scheme to approximate the Caputo fractional derivative 1 2 ( D t α 0 C f ( t k ) + D t α 0 C f ( t k − 1 ) ) , k = 1 , 2 , … , N , with the convergence order O ( Δ t 4 − α ) , α ∈ ( 1 , 2 ) is obtained when f ‴ ( t 0 ) = 0 , where Δt denotes the time step size. Based on this scheme we introduce a finite difference method for solving fractional diffusion wave equation with the convergence order O ( Δ t 4 − α + h 2 ) , where h denotes the space step size. Numerical examples are given to show that the numerical results are consistent with the theoretical results. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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