Numerical simulation of fractional power diffusion biosensors

Abstract

The main aim of this paper is to propose new mathematical models for simulation of biosensors and to construct and investigate discrete methods for the efficient solution of the obtained systems of nonlinear PDEs. The classical linear diffusion operators are substituted with nonlocal fractional powers of elliptic operators. The splitting type finite volume scheme is used as a basic template for the introduction of new mathematical models. Therefore the accuracy of the splitting scheme is investigated and compared with the symmetric Crank-Nicolson scheme. The dependence of the approximation error on the regularity of the solution is investigated. Results of computational experiments for different values of fractional parameters are presented and analysed.