Variable time step size application in implicit finite difference schemes when modelling operation of biosensors

• Published in: Lietuvos matematikos rinkinys Vol. 55; no. B
• Main Authors: Kurbanov, Arsenij, Ašeris, Vytautas
• Format: Journal Article
• Language: English
• Published: Vilniaus universiteto leidykla / Vilnius University Press 20.12.2014; Vilnius University Press
• Subjects: biosensor; implicit finite difference scheme; mathematical modelling; variable time step size; neišreikštinė baigtinių skirtumų schema; biosensor; mathematical modelling; matematinis modeliavimas; kintamas laiko žingsnis; biojutiklis; variable time step size; implicit finite difference scheme
• ISSN: 0132-2818; 2335-898X; 2335-898X
• DOI: 10.15388/LMR.B.2014.13

The operation of biosensors is described by mathematical models with reaction-diffusion equations. Due to non-linear reaction members, these models are solved using numerical methods, which often are a very time-consuming. The goal is to propose variable time step size algorithm which would reduce required calculations while preserving the accuracy of results. The proposed algorithm was applied to two biosensor models: with different diffusion and reaction. The applications of this algorithm are wide, because it is based on a few basic requirements, which are true for most biosensors models. The recommendations were made for choosing optimal algorithm parameters in general case. Algorithms efficiency was found to be dependent on mathematical models reaction part. Although the algorithm does reduce step count for all analyzed model parameters, the step count decrease ranges from 30% to tens of millions times.