A system of partial differential equations is used to model the dissemination of the Human Immunodeficiency Virus (HIV) in CD4+T cells within lymph nodes. Besides diffusion terms, the model also includes a time-delay dependence to describe the time lag required by the immunologic system to...

In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the...

Particle filters are numerical methods for approximating the solution of the filtering problem which use systems of weighted particles that (typically) evolve according to the law of the signal process. These methods involve a corrective/resampling procedure which eliminates the particles that...

Almost nothing decisive has been said about collocation methods for solving SPDEs. Among the best of such SPDEs the Burgers equation shows a prototypical model for describing the interaction between the reaction mechanism, convection effect, and diffusion transport. This paper discusses spectral...

In this dissertation we price European and American vanilla and barrier options assuming that the underlying follows the variance gamma process. We solve numerically the problem implementing a finite difference algorithm and we present numerical experiments on the option pricing. This...

The purpose of this paper is to present some numerical tools which facilitate the interpretation of simulation or data fitting results and which allow computation of optimal experimental designs. They help to validate mathematical models describing the dynamical behavior of a biological,...

We propose a class of finite volume methods for the discretization of time-dependent multidimensional hyperbolic systems in divergence form on unstructured grids. We discretize the divergence of the flux function by a cell-centered finite volume method whose spatial accuracy is provided by...