A A cubic B-spline collocation method for numerically solving fractional diffusion equations used in modelling dye-sensitized solar cells

Abstract

As part of the third generation of solar cells, dye-sensitized solar cells (DSSCs) are a novel, cost effective solution to the renewable energy problem. Mathematical modelling provides unique insight into operating DSSCs efficiently, particularly in the role of diffusion in the nanoporous semiconductor of the device. A recently published fractional diffusion model explores the link between the electron density of DSSCs and the porosity of the semiconductor. In this article, we solve the fractional diffusion model numerically using cubic B-splines to discretise space and an implicit finite difference scheme to discretise time. We compute the error by a standard collocation method.

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