An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an auxiliary Cauchy problem for a pseudo-parabolic equation. Unconditionally stable vector additive schemes (splitting schemes) are constructed. Numerical resul...

In the present work, the Roe, the Steger and Warming, the Van Leer, the Chakravarthy and Osher, the Harten, the Frink, Parikh and Pirzadeh, the Liou and Steffen Jr. and the Radespiel and Kroll schemes are implemented, on a finite volume context and using an upwind structured spatial discretization, to solve the Euler equations in the three-dimensional space. The Roe, the Harten, the Chakravarth...

In the present work, the Roe, the Steger and Warming, the Van Leer, the Harten, the Frink, Parikh and Pirzadeh, the Liou and Steffen Jr. and the Radespiel and Kroll schemes are implemented, on a finite volume context and using an upwind and unstructured spatial discretization, to solve the Euler equations in the three-dimensional space. The Roe, the Harten, and the Frink, Parikh and Pirzadeh sc...

Global Krylov subspace methods are the most efficient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose the nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as an inner iteration to approximate each outer iterate, while each...

The aim of this paper is to develop a mathematical model to simulate mosquito dispersal and its control taking into account environmental parameters, like wind, temperature, or landscape elements. We particularly focus on Aedes albopictus mosquito which is now recognized as a major vector of human arboviruses, like chikungunya, dengue, or yellow fever. One way to prevent those epidemics is to c...

An exact form is presented for the axial-vector Bethe-Salpeter equation, which is valid when the quark-gluon vertex is fully dressed. A Ward-Takahashi identity for the Bethe-Salpeter kernel is derived therefrom and solved for a class of dressed quark-gluon-vertex models. The solution provides a symmetry-preserving closed system of gap and vertex equations. The analysis can be extended to the ve...

Numerical simulations of a spacecraft at reentry conditions are presented. The fluid at such conditions is modeled as a reacting gas in thermal and chemical nonequilibrium. The reacting gas is modeled using a standard finite rate chemistry model for air. A twotemperature model is used to account for the thermal nonequilibrium effects. The finitevolume method is used to solve the set of differen...

We construct a second-order continuum traffic model by using an iterative procedure in order to derive a constitutive relation for the traffic pressure which is similar to the Navier–Stokes equation for ordinary fluids. Our second-order traffic model represents an improvement on the traffic model suggested by Kerner and Konhäuser since the iterative procedure introduces, in the constitutive rel...

In this paper, we present an efficient numerical method for multiphase image segmentation using a multiphase-field model. The method combines the vector-valued Allen– Cahn phase-field equation with initial data fitting terms containing prescribed interface width and fidelity constants. An efficient numerical solution is achieved using the recently developed hybrid operator splitting method for ...