1. Numerical analysis of light-controlled drug delivery systems.
- Author
-
Ferreira, J.A., Gómez, H.P., and Pinto, L.
- Subjects
- *
NUMERICAL analysis , *DRUG delivery systems , *FINITE difference method , *DRUG analysis , *NONLINEAR systems , *MATHEMATICAL models - Abstract
In this paper, we solve a non-linear reaction–diffusion system with Dirichlet–Neumann mixed boundary conditions using a finite difference method (FDM) in space and the implicit midpoint method in time. This type of system appears, e.g., in the mathematical modeling of light-controlled drug delivery. One of the key results of this paper is the proof that the method has superconvergence second-order in space in a discrete H 1 -norm and optimal second-order convergence in time in a discrete L 2 -norm. Our result relies on the direct analysis of a suitable error equation, avoiding the classic construction of consistency plus stability implies convergence. One advantage of such an analysis technique is the establishment of the method's non-linear stability in an elegant way. Numerical examples support the theoretical convergence result. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF