23 papers · ranked by Valyu relevance
Inés Gonzalez Pepe, Yohan Chatelain, Gregory Kiar, Tristan Glatard + 1 more
'Kathiravan Srinivasan'] Convolutional neural networks (CNNs) are currently among the most widely-used deep neural network (DNN) architectures available and achieve state-of-the-art performance for many problems. Originally applied to computer vision tasks, CNNs work well with any data with a spatial relationship…
R. Corban Harwood, Mitch Main
This paper investigates oscillation-free stability conditions of numerical methods for linear parabolic partial differential equations with some example extrapolations to nonlinear equations. Not clearly understood, numerical oscillations can create infeasible results. Since oscillation-free behavior is not ensured by…
Guihong Wang, Yuqing Li, T. Luo, Zheng Ma + 2 more
'Guang Lin'] In this note, 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 sufficient conditions for the stability and convergence of some common…
Carlos Beltrán, Vanni Noferini, Nick Vannieuwenhoven
As computers became increasingly common tools for engineers, mathematicians, and scientists, the accuracy of numerical computations in floating-point arithmetic has been of great interest. It was realized early in the history of numerical analysis that mathematically equivalent algorithms can nevertheless behave in…
Luke Shaw
A numerical integrator for ˙x = f(x) is called stable if, when applied to the 1D Dahlquist test equation ˙x = λx, λ ∈ C with fixed timestep h > 0, the numerical solution remains bounded as the number of steps tends to infinity. It is well known that no explicit integrator may remain stable beyond certain limits in λ.…
Lun-Shin Yao
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 required to satisfactorily approximate a differential derivative by its…
Aslam Abdullah
— Research on numerical stability of difference equations has been quite intensive in the past century. The choice of difference schemes for the derivative terms in these equations contributes to a wide range of the stability analysis issues - one of which is how a chosen scheme may directly or indirectly contribute to…
Ibrahim Karatay, Serife R. Bayramoglu
A high-order finite difference scheme is proposed for solving time fractional heat equations. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme a new second-order discretization, which is based on Crank-Nicholson method, is applied for the time fractional part and…
Yu Zhang, Longsuo Li
In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the…
Authors not listed
The rapid growth of worldwide computing power has transformed in silico chemistry into a discipline that is integrated into the daily work of many chemists. Nowadays, researchers find it increasingly straightforward to predict a wide range of molecular properties and chemi- cal processes at reasonable computational…
Gemeda Tolessa Lubo, Gemechis File Duressa
Objectives The main aim of this paper is to develop a linear B-spline finite element method for solving generalized diffusion equations with delay. The linear B-spline basis function is used to discretize the space variable. The time discretization process is based on Crank-Nicolson. The benefit of the scheme is that…
Nazar Ismailov, Nikolay Tschur, Georgii Kazantsev, Sergey Lobov + 1 more
A nonlinear mathematical model describing the vertical motion of a biomimetic underwater vehicle equipped with a swim bladder is developed. For a passive bladder that changes its volume under hydrostatic pressure, the system can achieve depth stabilization through a speed-induced mechanism when the lever-arm geometry…
Gianmarco Ducci, Gennaro Vitucci, Philippe Chatelain, Renaud Ronsse
Migratory birds travel over impressively long distances. Consequently, they have to adopt flight regimes being both efficient - in order to spare their metabolic resources - and robust to perturbations. This paper investigates the relationship between both aspects, i.e. mechanical performance and stability in flapping…
Dinshaw S. Balsara, Roger Käppeli
This paper examines a class of involution-constrained PDEs where some part of the PDE system evolves a vector field whose curl remains zero or grows in proportion to specified source terms. Such PDEs are referred to as curl-free or curl-preserving, respectively. They arise very frequently in equations for…
Humaira Farzana, Samir Kumar Bhowmik, Md. Shafiqul Islam
The numerical approximation of eigenvalues of higher even order boundary value problems has sparked a lot of interest in recent years. However, it is always difficult to deal with higher-order BVPs because of the presence of boundary conditions. The objective of this work is to investigate a few higher order eigenvalue…
José Guadalupe Rosas Jiménez, Balázs Fábián, Gerhard Hummer
The need for short time steps currently limits routine atomistic molecular dynamics (MD) simulations to the microsecond timescale. For long time steps, the numerical integration of the equations of motion becomes unstable, resulting in catastrophic crashes. Here, we combine mass repartitioning and rescaling to…
Liru Mu, Xinlong Feng, José F. F. Mendes
In this paper, the radial basis function finite difference method is used to solve two-dimensional steady incompressible Navier-Stokes equations. First, the radial basis function finite difference method with polynomial is used to discretize the spatial operator. Then, the Oseen iterative scheme is used to deal with…
Jian Jin, Dinant Kistemaker, Jaap H. van Dieën, Andreas Daffertshofer + 1 more
Identification of individuals at risk of falling is important when designing fall prevention methods. Current measures that estimate gait stability and robustness appear limited in predicting falls in older adults. Inspired by recent findings on changes in phase-dependent local stability within a gait cycle, we devised…
Matteo Cagiada, Sergey Ovchinnikov, Kresten Lindorff-Larsen
While there has been substantial progress in our ability to predict changes in protein stability due to amino acid substitutions, progress has been slower in methods to predict the absolute stability of a protein. Here we show how a generative model for protein sequence can be leveraged to predict absolute protein…
Hendrik Reimann, Sjoerd M. Bruijn
The walking human body is mechanically unstable. Loss of stability and falling is more likely in certain groups of people, such as older adults or people with neuromotor impairments, as well as in certain situations, such as when experiencing conflicting or distracting sensory inputs. Stability during walking is often…
Lakshdeep Gill, Andrew H. Huntley, Avril Mansfield
This study aimed to determine the validity of the centre of mass position (COM) position and extrapolated COM (XCOM), relative to the base of support, for predicting stability during a walking task where the base of support is constrained. Nine young healthy participants walked on a narrow beam. Three-dimensional…
Authors not listed
Free energy calculations based on molecular dynamics simulations offer a quantitative assessment of biomolecule binding and stability. This chapter discusses accurately estimating the free energy differences employing nonequilibrium alchemy. We cover the theoretical background, technical aspects of free energy…
Kasper Tolborg, Johan Klarbring, Alex M. Ganose, Aron Walsh
What is the likelihood that a hypothetical material - the combination of a composition and crystal structure - can be formed? Underpinning the reliability of predictions for local or global crystal stability is the choice of thermodynamic potential. Here, we discuss recent advances in free energy descriptions for…