1. A numerical scheme for a partial differential system motivated by light-triggered drug delivery.
- Author
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Ferreira, J.A., Gómez, H.P., and Pinto, L.
- Subjects
- *
FINITE difference method , *PARTIAL differential equations - Abstract
• Study of a system of quasilinear PDEs that can be used to model drug release from a polymeric structure enhanced by light. • A numerical scheme to compute the numerical solution of the IBVP based on the system of PDEs is proposed. • The theoretical support (stability and convergence) under weaker assumptions than those usually used is developed. • Numerical results illustrating the theoretical results established are provided. • A comparation between experimental data and simulation results is also presented. In this paper, we analyze a numerical scheme for a nonlinear coupled system of partial differential equations. Our study is motivated by the mathematical modeling of light-triggered drug delivery, a technique that can have a significant impact on cancer treatment. The numerical scheme combines a finite difference method (FDM) in space with an implicit-explicit (IMEX) method in time. For the main variable of interest - free drug concentration - we prove that the scheme is second-order supraconvergent in space in a discrete H 1 -norm and first-order convergent in time in a discrete L 2 -norm. We give numerical results illustrating the theoretical findings and computational simulations based on a laboratory experiment concerned with light-triggered drug delivery. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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