Journal
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
Volume 56, Issue 1-2, Pages 391-410Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s12190-016-1079-7
Keywords
Variable order derivative; Crank-Nicolson finite difference; Mobile-immobile advection-dispersion equation; Stability results; Error estimates; Numerical examples
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Funding
- National Natural Science Foundation of China [91130010, 11471194, 11571115]
- National Science Foundation [DMS-1216923]
- OSD/ARO MURI Grant [W911NF-15-1-0562]
- National Science and technology major projects of China [2011ZX05052, 2011ZX05011-004]
- Natural Science Foundation of Shandong Province of China [ZR2011AM015]
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A Crank-Nicolson finite difference scheme to solve a time variable order fractional mobile-immobile advection-dispersion equation is introduced and analyzed. Some a priori estimates of discrete L-2-norm with order of convergence O(tau + h(2)) are established on uniform grids where tau and h are the steps sizes in time and space. Stability and convergence of the numerical solutions are presented in detail. Numerical examples are provided to verify the theoretical analysis.
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