In this paper, we address the problem of modeling fish population movements. We first consider a description of movements at the level of individuals. An individual-based model is formulated as a biased random walk model in which the velocity of each fish has both a deterministic and a stochastic component. These components are function of a habitat suitability index, h, and its spatial gradien...

A parallel time integration method for nonlinear partial differential equations is proposed. It is based on a new implementation of the Paraexp method for linear partial differential equations (PDEs) employing a block Krylov subspace method. For nonlinear PDEs the algorithm is based on our Paraexp implementation within a waveform relaxation. The initial value problem is solved iteratively on a ...

We present a fourth-order accurate algorithm for solving Poisson’s equation, the heat equation, and the advection-diffusion equation on a hierarchy of block-structured, adaptively refined grids. For spatial discretization, finite-volume stencils are derived for the divergence operator and Laplacian operator in the context of structured adaptive mesh refinement and a variety of boundary conditio...

We consider a Fisher-KPP equation with density-dependent diffusion and advection, arising from a chemotaxis-growth model. We study its behavior as a small parameter, related to the thickness of a diffuse interface, tends to zero. We analyze, for small times, the emergence of transition layers induced by a balance between reaction and drift effects. Then we investigate the propagation of the lay...

It is the objective to provide a mathematical treatment of non-homogeneous and non-lipschitz reaction problem with non-linear diffusion advection operator, so that it can be applied fire extinguishing process in aerospace. The main findings are related existence characterization finite propagation support emerges virtue formulation. provided precise assessment on different times asso...

In this paper, a new derivation of a uniformly-convergent, second-order method for singularly-perturbed, linear ordinary differential equations based on the freezing of the coefficients of the differential equation, and integration of the resulting equations subject to continuity and smoothness conditions at the nodes, is presented. The derivation presented here is compared with others based on...