Journal
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
Volume 92, Issue 1, Pages 167-180Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207160.2014.887702
Keywords
65M06; 65M12; stability; reaction-subdiffusion equation; Caputo derivative; Fourier method; compact difference method; Neumann boundary value condition; convergence
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Funding
- Natural Science Foundation of China [11372170]
- Shanghai Municipal Education Commission [12ZZ084]
- grant of 'The First-class Discipline of Universities in Shanghai'
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In this paper, we derive a high-order compact finite difference scheme for solving the reaction-subdiffusion equation with Neumann boundary value condition. The L1 method is used to approximate the temporal Caputo derivative, and the compact difference operator is applied for spatial discretization. We prove that the compact finite difference method is unconditionally stable and convergent with order O(tau(2-alpha)+h(4)) in L-2 norm, where tau, alpha, and h are the temporal step size, the order of time fractional derivative and the spatial step size, respectively. Finally, some numerical experiments are carried out to show the effectiveness of the proposed difference scheme.
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