Results 221 to 230 of about 2,992 (267)

Molecular dynamics by the Backward‐Euler method

Communications on Pure and Applied Mathematics, 1989
AbstractThis paper introduces a new computational method for molecular dynamics. The method combines the Backward‐Euler scheme for the solution of stiff differential equations with a Langevin‐equation approach to the establishment of thermal equilibrium. The method allows the user to choose a cutoff frequency ωc.
Peskin, Charles S., Schlick, Tamar
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Backward Euler and other methods for simulating molecular fluids

The Journal of Chemical Physics, 1995
Two implementations of the backward Euler method for simulating molecular fluids are compared with Brownian dynamics and molecular dynamics simulations of a single diatomic molecule, liquid argon, a single butane molecule, and liquid butane. By comparison with standard molecular dynamics results, backward Euler simulations give different thermodynamic ...
Jian Wu, Robert O. Watts
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General decay stability of backward Euler–Maruyama method for nonlinear stochastic integro-differential equations

Applied Mathematics Letters, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Linna Liu, Feiqi Deng, Boyang Qu, Jianyin Fang   +3 more
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On the Backward Euler Method for Parabolic Equations with Rough Initial Data

SIAM Journal on Numerical Analysis, 1982
The backward Euler method is applied for the discretization in time of a general homogeneous parabolic equation in weak form. A short proof is given that, with k the time step, the norm of the error at time t is bounded by $Ckt^{ - 1} $ times the norm of the initial data.
Huang, Mingyou, Thomee, Vidar
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Stability of backward Euler multirate methods and convergence of waveform relaxation

BIT, 1992
Ideally, a numerical method for ordinary differential equations is stable if successive approximations decrease for each problem which has a decaying solution. Often this is interpreted in practice as requiring that a norm (usually an inner-product norm) of the difference between two approximations is non-increasing for a class of problems identified ...
Sand, J., Skelboe, Stig
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Invariant measure of the backward Euler method for stochastic differential equations driven by α$$ \alpha $$‐stable process

Mathematical Methods in the Applied Sciences, 2022
The backward Euler method is employed to approximate the invariant measure of a class of stochastic differential equations (SDEs) driven by ‐stable processes. The existence and uniqueness of the numerical invariant measure are proved. Then the numerical invariant measure is shown to converge to the underlying invariant measure.
Yanan Jiang, Liangjian Hu, Can Lv, Jianqiu Lu   +3 more
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A class of the backward Euler's method for initial value problems

Research Journal of Engineering and Technology, 2015
In this paper, we propose a class of the backward Euler's method for the numerical solution of initial value problems of ordinary differential equations. The proposed class is constructed by considering a suitable interpolating function. The accuracy and stability of the proposed class are considered.
Gurjinder Singh, V. Kanwar, Saurabh Bhatia   +2 more
openaire   +1 more source

Analysis of the backward‐euler/langevin method for molecular dynamics

Communications on Pure and Applied Mathematics, 1990
AbstractThis paper develops the theory of a recently introduced computational method for molecular dynamics. The method in question uses the backward‐Euler method to solve the classical Langevin equations of a molecular system. Parameters are chosen to produce a cutoff frequency ωc, which may be set equal to kT/h to simulate quantum‐mechanical effects.
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Time filtered second order backward Euler method for EMAC formulation of Navier-Stokes equations

Journal of Mathematical Analysis and Applications, 2022
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Demir, Medine, Çıbık, Aytekin, Kaya, Songul   +2 more
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Backward Euler method for stochastic differential equations with non-Lipschitz coefficients driven by fractional Brownian motion

BIT Numerical Mathematics, 2023
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Hao Zhou, Yaozhong Hu, Yanghui Liu
openaire   +2 more sources