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

Abstract

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.

Keywords

• biosensor
• mathematical modelling
• implicit finite difference scheme
• variable time step size