Journal
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
Volume 95, Issue 2, Pages 396-411Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207160.2017.1290434
Keywords
Second order; new derivative; quasilinear; fractional mobile; immobile transport model; estimates
Categories
Funding
- National Natural Science Foundation of China [91630207, 11471194, 11571115]
- National Science Foundation [DMS-1620194]
- OSD/ARO MURI [W911NF-15-1-0562]
- National Science and Technology Major Project of China [2011ZX05052, 2011ZX05011-004]
- Shandong Provincial Natural Science Foundation, China [ZR2011AM015]
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Recently, Caputo and Fabrizio introduce a new derivative with fractional order which has the ability to describe the material heterogeneities and the fluctuations of different scales. In this article, a finite difference scheme to solve a quasilinear fractal mobile/immobile transport model based on the new fractional derivative is introduced and analysed. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. Some a priori estimates of discrete are established on uniform partition. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.
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