Abstract
AbstractWe consider new numerical schemes to solve two different systems of nonlinear fractional reaction subdiffusion equations. These systems of equations model the reversible reaction $$A+B \rightleftharpoons C$$
A
+
B
⇌
C
in the presence of anomalous subdiffusion. The first model is based on the Henry & Wearne [1] model where the reaction term is added to the subdiffusion equation. The second model is based on the model by Angstmann, Donnelly & Henry [2] which involves a modified fractional differential operator. For both models the Keller Box method [3] along with a modified L1 scheme (ML1), adapted from the Oldham and Spanier L1 scheme [4], are used to approximate the spatial and fractional derivatives respectively. Numerical prediction of both models were compared for a number of examples given the same initial and boundary conditions and the same anomalous exponents. From the results, we see similar short time behaviour for both models predicted. However for long times the solution of the second model remains positive whilst the Henry & Wearne based–model predictions may become negative.
Funder
Australian Research Council
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference37 articles.
1. Henry, B.I., Wearne, S.L.: Fractional reaction-diffusion. Physica A: Statistical Mechanics and its Applications 276(3), 448–455 (2000)
2. Angstmann, C.N., Donnelly, I.C., Henry, B.I.: Continuous time random walks with reactions forcing and trapping. Mathematical Modelling of Natural Phenomena 8(2), 17–27 (2013)
3. Keller, H.B.: Numerical Solutions of Partial Differential Equations II, chap. A new difference scheme for parabolic problems, pp. 327–350. Academic Press, New York (1971)
4. Oldham, K., Spanier, J.: The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order. Elsevier, Netherlands (1974)
5. Seki, K., Wojcik, M., Tachiya, M.: Fractional reaction-diffusion equation. The Journal of Chemical Physics 119(4), 2165–2170 (2003)
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