Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations

Article


Osman, Sheelan and Langlands, Trevor. 2022. "Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations." Fractional Calculus and Applied Analysis. 25 (6), pp. 2166-2192. https://doi.org/10.1007/s13540-022-00096-2
Article Title

Numerical investigation of two models of nonlinear fractional reaction subdiffusion equations

ERA Journal ID39668
Article CategoryArticle
AuthorsOsman, Sheelan (Author) and Langlands, Trevor (Author)
Journal TitleFractional Calculus and Applied Analysis
Journal Citation25 (6), pp. 2166-2192
Number of Pages27
Year2022
Place of PublicationGermany
ISSN1311-0454
Digital Object Identifier (DOI)https://doi.org/10.1007/s13540-022-00096-2
Web Address (URL)https://link.springer.com/article/10.1007/s13540-022-00096-2
Abstract

We 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⇌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.

KeywordsFractional reaction subdiffusion equation; Keller Box method; Fractional calculus; L1 scheme; Nonlinear reactions systems
ANZSRC Field of Research 2020490299. Mathematical physics not elsewhere classified
490303. Numerical solution of differential and integral equations
490199. Applied mathematics not elsewhere classified
Byline AffiliationsSoran University, Iraq
School of Sciences
Institution of OriginUniversity of Southern Queensland
Funding source
Australian Research Council (ARC)
Grant ID
ARC120 DP130100595
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