Search

• 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]

Abstract: Integro-differential equations of Volterra type arise, naturally, in many applications such as for instance heat conduction in materials with memory, diffusion in polymers and diffusion in porous media. The aim of this paper is to study a finite difference discretization of the mentioned integro-differential equations. Second convergence order with respect to the norm is established which means that the discretization proposed is supraconvergent in finite difference methods language. As the finite difference method can be seen as a piecewise linear finite element method combined with special quadrature formulas, our result establishes the supercloseness of the gradient in the finite element language. Numerical results illustrating the discussed theoretical results are included. [Copyright &y& Elsevier]

In this paper we propose a numerical scheme for wave type equations with damping and space variable coefficients. Relevant equations of this kind arise for instance in the context of Maxwell's equations, namely, the electric potential equation and the electric field equation. The main motivation to study such class of equations is the crucial role played by the electric potential or the electric field in enhanced drug delivery applications. Our numerical method is based on piecewise linear finite element approximation and it can be regarded as a finite difference method based on non-uniform partitions of the spatial domain. We show that the proposed method leads to second order convergence, in time and space, for the kinetic and potential energies with respect to a discrete L 2 -norm. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study numerical methods for integro-differential initial boundary value problems that arise, naturally, in many applications such as heat conduction in materials with memory, diffusion in polymers and diffusion in porous media. Here, we propose finite difference methods to compute approximations for the continuous solutions of such problems. We analyze stability and study convergence for those methods. Supraconvergent estimates are obtained. As such methods can be seen as lumped mass methods, our supraconvergent result corresponds to a superconvergent property in the context of finite element methods. Numerical results illustrating the theoretical results are included. [ABSTRACT FROM AUTHOR]