Displaying similar documents to “Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers”

Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers

Sébastien Benzekry (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting...

Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers

Sébastien Benzekry (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting...

Numerical solution of a new hydrodynamic model of flocking

Kučera, Václav, Živčáková, Andrea

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This work is concerned with the numerical solution of a hydrodynamic model of the macroscopic behavior of flocks of birds due to Fornasier et al., 2011. The model consists of the compressible Euler equations with an added nonlocal, nonlinear right-hand side. As noticed by the authors of the model, explicit time schemes are practically useless even on very coarse grids in 1D due to the nonlocal nature of the equations. To this end, we apply a semi-implicit discontinuous Galerkin method...

A finite-volume scheme for a kidney nephron model

Aurélie Edwards, Nicolas Seguin, Magali Tournus (2012)

ESAIM: Proceedings

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We present a finite volume type scheme to solve a transport nephron model. The model consists in a system of transport equations with specific boundary conditions. The transport velocity is driven by another equation that can undergo sign changes during the transient regime. This is the main difficulty for the numerical resolution. The scheme we propose is based on an explicit resolution and is stable under a CFL condition which does not depend on the stiffness of source terms. ...