Dye-sensitized solar cells have generated diverse research directions, which include a mathematical model based on the diffusion of electrons in the conduction band of a nano-porous semiconductor (traditionally TiO\(_2\)). We solve the nonlinear diffusion equation under its boundary conditions, as stated by Anta et al. [J. Phys. Chem. B 110 (2006) pp 5372--5378]. We employ a standard finite difference method, a fourth order finite difference method scheme and a Runge--Kutta scheme. We calculate errors and evaluate the utility of each scheme as it applies to this boundary value problem.
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Numerical solutions for nonlinear partial differential equations arising from modelling dye-sensitized solar cells
