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We propose a local Legendre frame (LLF) method for function approximation from equispaced data on a finite interval. Motivated by the difficulty of stable high-order polynomial approximation at equispaced points, especially in the presence…

Numerical Analysis · Mathematics 2026-05-12 Benxue Gong , Zhenyu Zhao , Chenyang Wang

This work aims to construct an efficient and highly accurate numerical method to address the time singularity at $t=0$ involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The…

Numerical Analysis · Mathematics 2024-09-27 Sudarshan Santra , Ratikanta Behera

This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the…

Computational Engineering, Finance, and Science · Computer Science 2017-04-05 Fadime Bekmambetova , Xinyue Zhang , Piero Triverio

We extend the divergence preserving cut finite element method presented in [T. Frachon, P. Hansbo, E. Nilsson, S. Zahedi, SIAM J. Sci. Comput., 46 (2024)] for the Darcy interface problem to unfitted outer boundaries. We impose essential…

Numerical Analysis · Mathematics 2024-08-20 Thomas Frachon , Erik Nilsson , Sara Zahedi

In this paper we present a Local Fourier Analysis of a space-time multigrid solver for a hyperbolic test problem. The space-time discretization is based on arbitrarily high order discontinuous Galerkin spectral element methods in time and a…

Numerical Analysis · Mathematics 2021-12-07 Lea M. Versbach , Philipp Birken , Viktor Linders , Gregor Gassner

In this paper we are concerned with Trefftz discretizations of the time-dependent linear wave equation in anisotropic media in arbitrary space dimensional domains $\Omega \subset \mathbb{R}^d~ (d\in \mathbb{N})$. We propose two variants of…

Numerical Analysis · Mathematics 2022-02-08 Long Yuan

We analyse a Eulerian Finite Element method, combining a Eulerian time-stepping scheme applied to the time-dependent Stokes equations using the CutFEM approach with inf-sup stable Taylor-Hood elements for the spatial discretisation. This is…

Numerical Analysis · Mathematics 2022-08-12 Henry von Wahl , Thomas Richter , Christoph Lehrenfeld

Scale-resolving simulations of high Reynolds number incompressible flows are often limited by the Courant-Friedrichs-Lewy (CFL) stability restriction imposed by explicit time-stepping schemes, resulting in small time step sizes and long…

Fluid Dynamics · Physics 2026-04-20 Henrik Wüstenberg , Alexandra Liosi , Spencer J. Sherwin , Joaquim Peiró , David Moxey

Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles, suffer from very stiff differential equations plus multiscale challenges in space and time. The particles move smoothly through space until they interact almost…

Mathematical Software · Computer Science 2023-09-28 Peter Noble , Tobias Weinzierl

This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization…

Systems and Control · Electrical Eng. & Systems 2019-09-19 Pouya Badri , Mahdi Sojoodi

The paper is concerned with overlapping domain decomposition and exponential time differencing for the diffusion equation discretized in space by cell-centered finite differences. Two localized exponential time differencing methods are…

Numerical Analysis · Mathematics 2017-11-08 Thi-Thao-Phuong Hoang , Lili Ju , Zhu Wang

This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for finite-time stability are presented via state…

Optimization and Control · Mathematics 2018-06-25 Tianliang Zhang , Feiqi Deng , Weihai Zhang

We analyse the problem of stability of a continuous time linear switching system (LSS) versus the stability of its Euler discretization. It is well-known that the existence of a positive {\tau} for which the corresponding discrete time…

Optimization and Control · Mathematics 2014-07-16 Vladimir Yu. Protasov , Raphael M. Jungers

Efficient computation of all distinct solutions of nonlinear problems is essential in many scientific and engineering applications. Although high-order parallel iterative schemes offer fast convergence, their practical performance is often…

Numerical Analysis · Mathematics 2026-01-21 Mudassir Shams , Andrei Velichko , Bruno Carpentieri

Time series classification is crucial for numerous scientific and engineering applications. In this article, we present a numerically efficient, practically competitive, and theoretically rigorous classification method for distinguishing…

Methodology · Statistics 2025-07-11 Chen Qian , Xiucai Ding , Lexin Li

Discontinuous Galerkin (DG) methods for hyperbolic partial differential equations (PDEs) with explicit time-stepping schemes, such as strong stability-preserving Runge-Kutta (SSP-RK), suffer from time-step restrictions that are…

Numerical Analysis · Mathematics 2019-03-11 Pierson T. Guthrey , James A. Rossmanith

An extension of the two-step staggered time discretization of linear elastodynamics in stress-velocity form to systems involving internal variables subjected to a possibly non-linear dissipative evolution is proposed. The original scheme is…

Numerical Analysis · Mathematics 2020-06-11 Tomáš Roubíček , Chrysoula Tsogka

A time domain system of equations is proposed to model elastic wave propagation in an unbounded two-dimensional anisotropic solid using perfectly matched layer (PML). Starting from a system of first-order frequency domain stress-velocity…

Computational Physics · Physics 2013-12-16 Hisham Assi , Richard S. C. Cobbold

We develop a parabolic inf-sup theory for a modified TraceFEM semi-discretization in space of the heat equation posed on a stationary surface embedded in $\mathbb{R}^n$. We consider the normal derivative volume stabilization and add an…

Numerical Analysis · Mathematics 2024-09-24 Lucas Bouck , Ricardo H. Nochetto , Mansur Shakipov , Vladimir Yushutin

Stability and convergence of full discretizations of various surface evolution equations are studied in this paper. The proposed discretization combines a higher-order evolving-surface finite element method (ESFEM) for space discretization…

Numerical Analysis · Mathematics 2018-02-08 Balázs Kovács , Christian Lubich