Related papers: Von Neumann Stability Analysis for Multi-level Mul…
In this manuscript, we present the development of implicit and implicit-explicit ADER and DeC methodologies within the DeC framework using the two-operators formulation, with a focus on their stability analysis both as solvers for ordinary…
We consider the implementation of the split-step method where the linear part of the nonlinear Schr\"odinger equation is solved using a finite-difference discretization of the spatial derivative. The von Neumann analysis predicts that this…
The time-dependent equations of computational electrodynamics (CED) are evolved consistent with the divergence constraints. As a result, there has been a recent effort to design finite volume time domain (FVTD) and discontinuous Galerkin…
Von Neumann established that discretized algebraic equations must be consistent with the differential equations, and must be stable in order to obtain convergent numerical solutions for the given differential equations. The "stability" is…
We present compact semi-implicit finite difference schemes on structured grids for numerical solutions of the advection by an external velocity and by a speed in normal direction that are applicable in level set methods. The most involved…
This paper presents three main contributions to the field of multi-step system identification. First, drawing inspiration from Neural Network (NN) training, it introduces a tool for solving identification problems by leveraging first-order…
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…
The Allen-Cahn equation is a fundamental model for phase transitions, offering critical insights into the dynamics of interface evolution in various physical systems. This paper investigates the stability and robustness of frequently…
In this paper we have studied subgrid multiscale stabilized formulation with dynamic subscales for non-Newtonian Casson fluid flow model tightly coupled with variable coefficients ADR ($VADR$) equation. The Casson viscosity coefficient is…
In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some…
Weighted averaged finite difference methods for solving fractional diffusion equations are discussed and different formulae of the discretization of the Riemann-Liouville derivative are considered. The stability analysis of the different…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
This paper considers a two-step fourth-order modified explicit Euler/Crank-Nicolson numerical method for solving the time-variable fractional mobile-immobile advection-dispersion model subjects to suitable initial and boundary conditions.…
Divergence and vorticity damping, which operate upon horizontal divergence and relative vorticity, are explicit diffusion mechanisms used in dynamical cores to ensure stability. To avoid numerical blow-up from excessively strong diffusion,…
The stability of five finite difference-time domain (FD-TD) schemes coupling Maxwell equations to Debye or Lorentz models have been analyzed in [1] (P.G. Petropoulos, "Stability and phase error analysis of FD-TD in dispersive dielectrics",…
Stability properties of the well-known Fourier split-step method used to simulate a soliton and similar solutions of the nonlinear Dirac equations, known as the Gross--Neveu model, are studied numerically and analytically. Three distinct…
This paper presents a novel method for stability analysis of a wide class of linear, time-delay systems (TDS), including retarded non-neutral ones, as well as those incorporating incommensurate and distributed delays. The proposed method is…
This work is devoted to the development of a distributionally robust active fault diagnosis approach for a class of nonlinear systems, which takes into account any ambiguity in distribution information of the uncertain model parameters.…
The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and…
We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…