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 ID | 39668 |
| Article Category | Article |
| Authors | Osman, Sheelan (Author) and Langlands, Trevor (Author) |
| Journal Title | Fractional Calculus and Applied Analysis |
| Journal Citation | 25 (6), pp. 2166-2192 |
| Number of Pages | 27 |
| Year | 2022 |
| Place of Publication | Germany |
| ISSN | 1311-0454 |
| 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. |
| Keywords | Fractional reaction subdiffusion equation; Keller Box method; Fractional calculus; L1 scheme; Nonlinear reactions systems |
| ANZSRC Field of Research 2020 | 490299. Mathematical physics not elsewhere classified |
| 490303. Numerical solution of differential and integral equations | |
| 490199. Applied mathematics not elsewhere classified | |
| Byline Affiliations | Soran University, Iraq |
| School of Sciences | |
| Institution of Origin | University of Southern Queensland |
| Funding source | Australian Research Council (ARC) Grant ID ARC120 DP130100595 |
Permalink -
https://research.usq.edu.au/item/q7wz4/numerical-investigation-of-two-models-of-nonlinear-fractional-reaction-subdiffusion-equations
Download files
Published Version
| Numerical investigation of two models.pdf | ||
| License: CC BY 4.0 | ||
| File access level: Anyone | ||
32
total views31
total downloads2
views this month2
downloads this month
Export as
Related outputs
Connecting community online and through partnership: A reflective piece
Pickstone, Leigh, Sharma, Ekta, King, Rachel, Galligan, Linda and Langlands, Trevor. 2022. "Connecting community online and through partnership: A reflective piece." International Journal for Students as Partners. 6 (2), pp. 114-120. https://doi.org/10.15173/ijsap.v6i2.4825Modern artificial intelligence model development for undergraduate student performance prediction: an investigation on engineering mathematics courses
Deo, Ravinesh C., Yaseen, Zaher Mundher, Al-Ansari, Nadhir, Nguyen-Huy, Thong, Langlands, Trevor and Galligan, Linda. 2020. "Modern artificial intelligence model development for undergraduate student performance prediction: an investigation on engineering mathematics courses." IEEE Access. 8, pp. 136697-136724. https://doi.org/10.1109/ACCESS.2020.3010938An implicit Keller Box numerical scheme for the solution of fractional subdiffusion equations
Osman, S. A and Langlands, T. A. M.. 2019. "An implicit Keller Box numerical scheme for the solution of fractional subdiffusion equations." Applied Mathematics and Computation. 348, pp. 609-626. https://doi.org/10.1016/j.amc.2018.12.015Numerical solution methods for fractional partial differential equations
Osman, Sheelan Abdulkader. 2017. Numerical solution methods for fractional partial differential equations. PhD Thesis Doctor of Philosophy. University of Southern Queensland. https://doi.org/10.26192/5c075fc8baf89From stochastic processes to numerical methods: a new scheme for solving reaction subdiffusion fractional partial differential equations
Angstmann, C. N., Donnelly, I. C., Henry, B. I., Jacobs, B. A., Langlands, T. A. M. and Nichols, J. A.. 2016. "From stochastic processes to numerical methods: a new scheme for solving reaction subdiffusion fractional partial differential equations." Journal of Computational Physics. 307, pp. 508-534. https://doi.org/10.1016/j.jcp.2015.11.053Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions
Langlands, Trevor, Henry, B. I. and Wearne, S. L.. 2009. "Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions." Journal of Mathematical Biology. 59 (6), pp. 761-808. https://doi.org/10.1007/s00285-009-0251-1A mathematical model for the proliferation, accumulation and spread of pathogenic proteins along neuronal pathways with locally anomalous trapping
Angstmann, C. N., Donnelly, I. C., Henry, B. I. and Langlands, T. A. M.. 2016. "A mathematical model for the proliferation, accumulation and spread of pathogenic proteins along neuronal pathways with locally anomalous trapping." Mathematical Modelling of Natural Phenomena (MMNP). 11 (3), pp. 142-156. https://doi.org/10.1051/mmnp/20161139Generalized continuous time random walks, master equations, and fractional Fokker-Planck equations
Angstmann, C. N., Donnelly, I. C., Henry, B. I., Langlands, T. A. M. and Straka, P.. 2015. "Generalized continuous time random walks, master equations, and fractional Fokker-Planck equations." SIAM Journal on Applied Mathematics. 75 (4), pp. 1445-1468. https://doi.org/10.1137/15M1011299Continuous-time random walks on networks with vertex- and time-dependent forcing
Angstmann, C. N., Donnelly, I. C., Henry, B. I. and Langlands, T. A. M.. 2013. "Continuous-time random walks on networks with vertex- and time-dependent forcing." Physical Review E. 88 (2). https://doi.org/10.1103/PhysRevE.88.022811Fractional cable equation models for anomalous electrodiffusion in nerve cells: finite domain solutions
Langlands, T. A. M., Henry, B. I. and Wearne, S. L.. 2011. "Fractional cable equation models for anomalous electrodiffusion in nerve cells: finite domain solutions." SIAM Journal on Applied Mathematics. 71 (4), pp. 1168-1203. https://doi.org/10.1137/090775920Fractional diffusion in force fields, fractional electro-diffusion and fractional chemotaxis diffusion
Langlands, Trevor, Henry, Bruce and Straka, Peter. 2010. "Fractional diffusion in force fields, fractional electro-diffusion and fractional chemotaxis diffusion." Henry, Bruce and Roberts, John (ed.) Dynamics Days Asia Pacific 6 Conference (DDAP6). Sydney, Australia 12 - 14 Jul 2010 Sydney, Australia.Anomalous subdiffusion with multispecies linear reaction dynamics
Langlands, Trevor, Henry, B. I. and Wearne, S. L.. 2008. "Anomalous subdiffusion with multispecies linear reaction dynamics." Physical Review B: Covering condensed matter and materials physics. 77, pp. 1-9. https://doi.org/10.1103/PhysRevE.77.021111Fractional cable models for spiny neuronal dendrites
Henry, B. I., Langlands, Trevor and Wearne, S. L.. 2008. "Fractional cable models for spiny neuronal dendrites." Physical Review Letters. 100 (12), pp. 1-4. https://doi.org/10.1103/PhysRevLett.100.128103Turing pattern formation with fractional diffusion and fractional reactions
Langlands, T. A. M., Henry, B. I. and Wearne, S. L.. 2006. "Turing pattern formation with fractional diffusion and fractional reactions." Journal of Physics: Condensed Matter. 19 (6), pp. 065115 -065134. https://doi.org/10.1088/0953-8984/19/6/065115Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations
Henry, B. I., Langlands, Trevor and Wearne, S. L.. 2006. "Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations." Physical Review E. 74 (3), pp. 1-15. https://doi.org/10.1103/PhysRevE.74.031116Solution of a modified fractional diffusion equation
Langlands, T. A. M.. 2006. "Solution of a modified fractional diffusion equation." Physica A: Statistical Mechanics and its Applications. 367, pp. 136-144. https://doi.org/10.1016/j.physa.2005.12.012Fractional Fokker-Planck equations for subdiffusion with space-and time-dependent forces
Henry, B. I., Langlands, T. A. M. and Straka, P.. 2010. "Fractional Fokker-Planck equations for subdiffusion with space-and time-dependent forces." Physical Review Letters. 105 (17), pp. 17062-1-170602-4. https://doi.org/10.1103/PhysRevLett.105.170602Fractional chemotaxis diffusion equations
Langlands, T. A. M. and Henry, B. I.. 2010. "Fractional chemotaxis diffusion equations." Physical Review E. 81 (5), pp. 1-12. https://doi.org/10.1103/PhysRevE.81.051102Optimal targeting of hepatitis C virus treatment among injecting drug users to those not enrolled in methadone maintenance programs
Zeiler, Irmgard, Langlands, Trevor, Murray, John M. and Ritter, Alison. 2010. "Optimal targeting of hepatitis C virus treatment among injecting drug users to those not enrolled in methadone maintenance programs." Drug and Alcohol Dependence. 110 (3), pp. 228-233. https://doi.org/10.1016/j.drugalcdep.2010.03.006An introduction to fractional diffusion
Henry, B. I., Langlands, Trevor and Straka, P.. 2010. "An introduction to fractional diffusion." Dewar, Robert L. and Detering, Frank (ed.) 22nd Canberra International Physics Summer School. Canberra, Australia 08 - 19 Dec 2008 Singapore. https://doi.org/10.1142/9789814277327_0002This item comprises data from the following sources: Scopus