Related papers: Provably Stable Full-Spectrum Dispersion Relation …
This paper focuses on providing the high order algorithms for the space-time tempered fractional diffusion-wave equation. The designed schemes are unconditionally stable and have the global truncation error $\mathcal{O}(\tau^2+h^2)$, being…
In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…
We consider a Poisson equation in $\mathbb R^d$ for the elliptic operator corresponding to an ergodic diffusion process. Optimal regularity and smoothness with respect to the parameter are obtained under mild conditions on the coefficients.…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
We propose two stable and one conditionally stable finite difference schemes of second-order in both time and space for the time-fractional diffusion-wave equation. In the first scheme, we apply the fractional trapezoidal rule in time and…
In this work we study the existence, uniqueness and polynomial stability of the pseudo almost periodic mild solutions of semi-linear diffusion equations with rough coefficients in certain interpolation spaces. First, we rewirte the…
We describe a method for removing the numerical errors in the modeling of linear evolution equations that are caused by approximating the time derivative by a finite difference operator. The method is based on integral transforms realized…
This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…
This work considers the variable-exponent fractional diffusion-wave equation, which describes, e.g. the propagation of mechanical diffusive waves in viscoelastic media with varying material properties. Rigorous numerical analysis for this…
In this article, we first obtain, for the Kolmogorov distance, an error bound between a tempered stable and a compound Poisson distribution and also an error bound between a tempered stable and an alpha stable distribution via Stein method.…
This paper addresses the existence and spectral stability of traveling fronts for nonlinear hyperbolic equations with a positive "damping" term and a reaction function of bistable type. Particular cases of the former include the relaxed…
Stability is an important aspect of numerical methods for hyperbolic conservation laws and has received much interest. However, continuity in time is often assumed and only semidiscrete stability is studied. Thus, it is interesting to…
The stability of nonlinear explicit difference schemes with not, in general, open domains of the scheme operators are studied. For the case of path-connected, bounded, and Lipschitz domains, we establish the notion that a multi-level…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
We study non-conforming grid interfaces for summation-by-parts finite difference methods applied to partial differential equations with second derivatives in space. To maintain energy stability, previous efforts have been forced to accept a…
We propose a new fully-discretized finite difference scheme for a quantum diffusion equation, in both one and two dimensions. This is the first fully-discretized scheme with proven positivity-preserving and energy stable properties using…
We analyse stability of observability estimates for solutions to wave and Scr\" odinger equations subjected to additive perturbations. The paper generalises the recent averaged observability/control result by allowing for systems consisting…
It is known that Flux Corrected Transport algorithms can produce entropy-violating solutions of hyperbolic conservation laws. Our purpose is to design flux correction with maximal antidiffusive fluxes to obtain entropy solutions of scalar…
A growing body of literature has been leveraging techniques of machine learning (ML) to build novel approaches to approximating the solutions to partial differential equations. Noticeably absent from the literature is a systematic…
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…