Related papers: Algebraic Stabilization of Explicit Numerical Inte…
The principle of detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process. For many real physico-chemical complex systems (e.g. homogeneous combustion, heterogeneous catalytic oxidation,…
An existing solvability result for relaxed one-sided Lipschitz algebraic inclusions is substantially improved. This enhanced solvability result allows the design of a very robust numerical method for the approximation of a solution of the…
Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
We propose a second order, fully semi-Lagrangian method for the numerical solution of systems of advection-diffusion-reaction equations, which employs a semi-Lagrangian approach to approximate in time both the advective and the diffusive…
This paper is concerned about the implicit-explicit (IMEX) methods for a class of dissipative wave systems with time-varying velocity feedbacks and nonlinear potential energies, equipped with different boundary conditions. Firstly, we…
In this work, we modify a continuous Galerkin discretization of a scalar hyperbolic conservation law using new algebraic correction procedures. Discrete entropy conditions are used to determine the minimal amount of entropy stabilization…
We study numerical methods for the nonlinear partial differential equation that governs the motion of level sets by affine curvature. We show that standard finite difference schemes are nonlinearly unstable. We build convergent finite…
In this paper we investigate a new class of implicit-explicit (IMEX) two-step methods of Peer type for systems of ordinary differential equations with both non-stiff and stiff parts included in the source term. An extrapolation approach…
In this work I discuss briefly the calculation of the algebraic entropy for systems of quad equations. In particular, I observe that since systems of multilinear equations can have algebraic solution, in some cases one might need to…
Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints…
The computation of the radiative transfer equation is expensive mainly due to two stiff terms: the transport term and the collision operator. The stiffness in the former comes from the fact that particles (such as photons) travels at the…
Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…
We extend the notion of numerical stability of finite difference approximations to include hyperbolic systems that are first order in time and second order in space, such as those that appear in Numerical Relativity. By analyzing the symbol…
In this paper, we consider the problem of stabilizing discrete-time linear systems by computing a nearby stable matrix to an unstable one. To do so, we provide a new characterization for the set of stable matrices. We show that a matrix $A$…
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known…
The stable allocation problem is one of the broadest extensions of the well-known stable marriage problem. In an allocation problem, edges of a bipartite graph have capacities and vertices have quotas to fill. Here we investigate the case…
The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
In this preliminary work, we present nonstandard time-stepping strategies to solve differential equations based on the algebraic estimation method applied to the estimation of time-derivative, which provides interesting properties of…