Related papers: Numerical methods with controlled dissipation for …
Modeling of fluid flows requires corresponding adequate and effective approaches that would account for multiscale nature of the considered physics. Despite the tremendous growth of computational power in the past decades, modeling of fluid…
Several new methods of numerical integration of Cauchy problems with blow-up solutions for nonlinear ordinary differential equations of the first- and second-order are described. Solutions of such problems have singularities whose positions…
This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
This work is concerned with relaxation models arising from numerical schemes for hyperbolic-parabolic systems. Such models are a hyperbolic system with both the hyperbolic part and the stiff source term involving a small positive parameter,…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
Although stable solutions of dynamical systems are typically considered more important than unstable ones, unstable solutions have a critical role in the dynamical integrity of stable solutions. In fact, usually, basins of attraction…
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…
Extending our earlier work on Lax-type shocks of systems of conservation laws, we establish existence and stability of curved multidimensional shock fronts in the vanishing viscosity limit for general Lax- or undercompressive-type shock…
Many suspensions contain particles with complex shapes that are affected not only by hydrodynamics, but also by thermal fluctuations, internal kinematic constraints and other long-range non-hydrodynamic interactions. Modeling these systems…
This paper is devoted to the study of hyperbolic systems of linear partial differential equations perturbed by a Brownian motion. The existence and uniqueness of solutions are proved by an energy method. The specific features of this class…
We propose a new class of asymptotic preserving schemes to solve kinetic equations with mono-kinetic singular limit. The main idea to deal with the singularity is to transform the equations by appropriate scalings in velocity. In…
We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward stochastic differential equations (BSDEs) driven by L\`{e}vy…
This paper deals with the numerical (finite volume) approximation of reaction-diffusion systems with relaxation, among which the hyperbolic extension of the Allen--Cahn equation represents a notable prototype. Appropriate discretizations…
Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of…
In this paper a new semi-implicit relaxation scheme for the simulation of multi-scale hyperbolic conservation laws based on a Jin-Xin relaxation approach is presented. It is based on the splitting of the flux function into two or more…
We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…
A new approach to prevent spurious behavior caused by conventional shock-capturing schemes when solving stiff detonation waves problems is introduced in the present work. Due to smearing of discontinuous solution by the excessive numerical…
The weighted essentially non-oscillatory (WENO) methods are popular and effective spatial discretization methods for nonlinear hyperbolic partial differential equations. Although these methods are formally first-order accurate when a shock…
This study investigates numerical methods to solve nonlinear transport problems characterized by various sorption isotherms with a focus on the Freundlich type of isotherms. We describe and compare second order accurate numerical schemes,…