Validation of numerical solution of diffusive part in a reaction–diffusion model. (1st July 2017)

• Record Type: Journal Article
• Authors: Herrera-Hernández, E.C.; Núñez-López, M.; González-Calderón, J.A.
• Is Part Of: Computers & mathematics with applications. Volume 74:issue 1(2017)
• Page Start: 143
• Page End: 156
• Publication Date: 2017-07-01
• Subjects: Numerical validation -- Mass conservation -- Reaction–diffusion system -- Finite differences method -- Mean square displacement; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.01.013
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this work, we present a methodological procedure to validate the numerical solution of the diffusive part in a reaction–diffusion model. Uniform explicit finite differences method is used to generate the solution in a confined circular domain with boundary condition of zero flux. For the validation of the numerical solution, we consider three different criteria applied to normal diffusion and sub-diffusive cases: (i) the moments of concentration, ​(ii) decay of the concentration at the origin and (iii) the mass conservation. The numerical solution fulfills the validation criteria of moments and concentration decay at the origin only in the long-term. The mass conservation criterion is fulfilled when the initial condition is imposed close to the border, whereas when it is set near to the origin a dependence on the diffusion rate appears. Pattern formation is presented after validating the numerical solution for normal diffusive case. Good agreement of stationary spatial pattern against reported results is observed.