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The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…
In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…
It is often claimed that error cancellation plays an essential role in quantum chemistry and first-principle simulation for condensed matter physics and materials science. Indeed, while the energy of a large, or even medium-size, molecular…
We investigate the influence of numerical discretization errors on computed averages in a molecular dynamics simulation of TIP4P liquid water at 300 K coupled to different deterministic (Nos\'e-Hoover and Nos\'e-Poincar\'e) and stochastic…
The high accuracy exhibited by biological information transcription processes is due to kinetic proofreading, i.e., by a mechanism which reduces the error rate of the information-handling process by driving it out of equilibrium. We provide…
Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve associated local conservation laws and constraints very well in long time numerical simulations. Backward error analysis for PDEs, or the…
We propose an energy-optimized invariant energy quadratization method to solve the gradient flow models in this paper, which requires only one linear energy-optimized step to correct the auxiliary variables on each time step. In addition to…
We consider systematic numerical approximation of a viscoelastic phase separation model that describes the demixing of a polymer solvent mixture. An unconditionally stable discretisation method is proposed based on a finite element…
We consider the harmonic map heat flow problem for a corotational case. For discretization of this problem we apply a $H^1$-conforming finite element method in space combined with a semi-implicit Euler time stepping. The semi-implicit Euler…
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
Kinetic proofreading mechanisms explain the extraordinary accuracy observed in central biological events in terms of the enhanced specificity of substrate selection networks under a nonequilibrium environment. The nonequilibrium steady…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
In computational system biology, the mesoscopic model of reaction-diffusion kinetics is described by a continuous time, discrete space Markov process. To simulate diffusion stochastically, the jump coefficients are obtained by a…
In solid-state physics, energies of molecular systems are usually computed with a plane-wave discretization of Kohn-Sham equations. A priori estimates of plane-wave convergence for periodic Kohn-Sham calculations with pseudopotentials have…
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…
We revisit an algorithm by Skeel et al. for computing the modified, or shadow, energy associated with the symplectic discretization of Hamiltonian systems. By rephrasing the algorithm as a Richardson extrapolation scheme arbitrary high…
The Orthodox kinetic energy has, in fact, two hidden-variable components: one linked to the current (or Bohmian) velocity, and another linked to the osmotic velocity (or quantum potential), and which are respectively identified with phase…
A framework for exponential time discretization of the multilayer rotating shallow water equations is developed in combination with a mimetic discretization in space. The method is based on a combination of existing exponential time…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages…