Related papers: A Numerical Study of WENO Approximations to Sharp …
In this paper, we introduce a high-order accurate constrained transport type finite volume method to solve ideal magnetohydrodynamic equations on two-dimensional triangular meshes. A new divergence-free WENO-based reconstruction method is…
In this paper, we develop parametrized positivity satisfying flux limiters for the high order finite difference Runge-Kutta weighted essentially non-oscillatory (WENO) scheme solving compressible Euler equations to maintain positive density…
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…
We propose new fully discrete third-order accurate Active Flux and WENO methods based on truly multidimensional evolution operators for the two-dimensional acoustic equations. Building on the method of bicharacteristics, several approximate…
This paper establishes the spectral stability in exponentially weighted spaces of smooth traveling monotone fronts for reaction diffusion equations of Fisher-KPP type with nonlinear degenerate diffusion coefficient. It is assumed that the…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
We present a new finite difference shock-capturing scheme for hyperbolic equations on static uniform grids. The method provides selectable high-order accuracy by employing a kernel-based Gaussian Process (GP) data prediction method which is…
The recently proposed high-order TENO scheme [Fu et al., Journal of Computational Physics, 305, pp.333-359] has shown great potential in predicting complex fluids owing to the novel weighting strategy, which ensures the high-order accuracy,…
We are concerned with a class of degenerate diffusion equations with time delay describing population dynamics with age structure. In our recent study [{\em Nonlinearity}, 33 (2020), 4013--4029], we established the existence and uniqueness…
In this paper, we consider a reaction-diffusion system describing the propagation of flames under the assumption of ignition-temperature kinetics and fractional reaction order. It was shown in [3] that this system admits a traveling front…
A numerical study of the role of anomalous diffusion in front propagation in reaction-diffusion systems is presented. Three models of anomalous diffusion are considered: fractional diffusion, tempered fractional diffusion, and a model that…
In this paper, we propose a well-balanced fifth-order finite difference Hermite WENO (HWENO) scheme for the shallow water equations with non-flat bottom topography in pre-balanced form. For achieving the well-balance property, we adopt the…
We propose a way to maintain strong consistency and facilitate error analysis in the context of dissipation-based WENO stabilization for continuous and discontinuous Galerkin discretizations of conservation laws. Following Kuzmin and Vedral…
In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of reaction-diffusion equations, and we will apply our…
We propose a class of weighted compact central (WCC) schemes for solving hyperbolic conservation laws. The linear version can be considered as a high-order extension of the central Lax-Friedrichs (LxF) scheme and the central conservation…
We study a one-dimensional reaction-diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic (A + B -> 2B) and a cubic (A + 2B -> 3B) autocatalysis. The parameters of this system are the…
We consider bistable reaction-diffusion equations in funnel-shaped domains of R N made up of straight parts and conical parts with positive opening angles. We study the large time dynamics of entire solutions emanating from a planar front…
We introduce new adaptive artificial anti-diffusion (AAAD) methods for one- and two-dimensional hyperbolic systems of conservation laws. The key idea is to reduce the amount of numerical dissipation present in a given numerical method by…
The current paper is devoted to the investigation of wave propagation phenomenon in reaction-diffusion equations with ignition type nonlinearity in time heterogeneous and random media. It is proven that such equations in time heterogeneous…
Nonlinear fronts between spatially extended traveling wave convection (TW) and quiescent fluid and spatially localized traveling waves (LTWs) are investigated in quantitative detail in the bistable regime of binary fluid mixtures heated…