Journal
APPLIED NUMERICAL MATHEMATICS
Volume 134, Issue -, Pages 17-30Publisher
ELSEVIER
DOI: 10.1016/j.apnum.2018.07.001
Keywords
Fractional derivative; Diffusion-wave equation; Novel finite difference; Numerical experiments; Estimates
Categories
Funding
- National Natural Science Foundation of China [91630207, 11471194, 11571115]
- National Science Foundation [DMS-1216923]
- OSD/ARO MURI [W911NF-15-1-0562]
- National Science and technology major projects of China [2011ZX05052, 2011ZX05011-004]
- Natural Science Foundation of Shandong Province of China [ZR2011AM015]
- China Scholarship Council [201706220150, 201706220152]
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In this article, we consider initial and boundary value problems for the diffusion wave equation involving a Caputo fractional derivative (of order a, with 1 < alpha < 2) in time. A novel finite difference discrete scheme is developed for using discrete fractional derivative at time t(n) in which some new coefficients (k + 1/2)(2-alpha) (k - 1/2)(2-alpha) instead of (k + 1)(2-alpha) - k(2-alpha) are derived. Stability and convergence of the method are rigorously established. We prove that the novel discretization is unconditionally stable, and the optimal convergence orders O (tau(3-alpha) + h(2)) both in L-2 and L-infinity, are derived, where tau is the time step and h is space mesh size. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.
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