On the numerical schemes for Langevin-type equations

In this paper, a numerical approach is proposed based on the variation-of-constants formula for the numerical discretization Langevin-type equations. Linear and non-linear cases are treated separately. The proofs of convergence have been provided for the linear case, and the numerical implementation has been executed for the non-linear case. The order one convergence for the numerical scheme has been shown both theoretically and numerically. The stability of the numerical scheme has been shown numerically and depicted graphically.

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Numerical discretization of stochastic oscillators with generalized numerical integrators

Thermal Science ◽

10.2298/tsci200630008s ◽

2021 ◽

Vol 25 (Spec. issue 1) ◽

pp. 65-75

Author(s):

Ali Sirma ◽

Resat Kosker ◽

Muzaffer Akat

Keyword(s):

Numerical Experiments ◽

Numerical Scheme ◽

Additive Noise ◽

First Order ◽

Variation Of Constants Formula ◽

Variation Of Constants ◽

Numerical Integrators ◽

One Step ◽

Numerical Discretization ◽

Stochastic Oscillators

In this study, we propose a numerical scheme for stochastic oscillators with additive noise obtained by the method of variation of constants formula using generalized numerical integrators. For both of the displacement and the velocity components, we show that the scheme has an order of 3/2 in one step convergence and a first order in overall convergence. Theoretical statements are supported by numerical experiments.

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Some Remarks on the Stability Condition of Numerical Scheme of the KdV-type Equation

Journal of Mathematics Research ◽

10.5539/jmr.v9n4p11 ◽

2017 ◽

Vol 9 (4) ◽

pp. 11 ◽

Cited By ~ 1

Author(s):

Chun-Te Lee ◽

Jeng-Eng Lin ◽

Chun-Che Lee ◽

Mei-Li Liu

Keyword(s):

Stability Condition ◽

Numerical Scheme ◽

Kdv Equation ◽

Type Equation ◽

Stability Criteria ◽

Numerical Schemes ◽

The Kdv Equation ◽

The Stability ◽

Difference Fourier ◽

Central Finite Difference

This paper has employed a comparative study between the numerical scheme and stability condition. Numerical calculations are carried out based on three different numerical schemes, namely the central finite difference, fourier leap-frog, and fourier spectral RK4 schemes. Stability criteria for different numerical schemes are developed for the KdV equation, and numerical examples are put to test to illustrate the accuracy and stability between the solution profile and numerical scheme.

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Looking for Those Natural Numbers: Dimensionless Constants and the Idea of Natural Measurement

Science in Context ◽

10.1017/s0269889700001125 ◽

1992 ◽

Vol 5 (1) ◽

pp. 165-188 ◽

Cited By ~ 21

Author(s):

Philip Mirowski

Keyword(s):

20Th Century ◽

Numerical Scheme ◽

Mathematical Problem ◽

Natural Numbers ◽

Numerical Schemes ◽

Late 20Th Century ◽

Cultural Terms ◽

Societal Context ◽

History Of ◽

The Stability

The ArgumentMany find it “notoriously difficult to see how societal context can affect in any essential way how someone solves a mathematical problem or makes a measurement.” That may be because it has been a habit of western scientists to assert their numerical schemes were untainted by any hint of anthropomorphism. Nevertheless, that Platonist penchant has always encountered obstacles in practice, primarily because the stability of any applied numerical scheme requires some alien or external warrant.This paper surveys the history of measurement standards, physical dimensions and dimensionless constants as one instance of the quest to purge all anthropomorphic taint first in the metric system, then in the dimensions provided by the atom, then in physical constants intelligible to extraterrestrials, only then to end up back at overt anthropomorphism in the late 20th century. This suggests that the “naturalness” of natural numbers has always been conceptualized in locally contingent cultural terms.

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The Stability Analysis of a Class of Numerical Schemes for Partial Differential Systems

2019 Chinese Control Conference (CCC) ◽

10.23919/chicc.2019.8865584 ◽

2019 ◽

Author(s):

Xinrong Cong ◽

Shuxia Zhang ◽

Longsuo Li

Keyword(s):

Stability Analysis ◽

Numerical Schemes ◽

Partial Differential ◽

Differential Systems ◽

The Stability

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PARALLEL SOLVER FOR THE SIMULATIONS OF DETONATION WAVES ON UNSTRUCTURED GRIDS

NONEQUILIBRIUM PROCESSES: RECENT ACCOMPLISHMENTS ◽

10.30826/nepcap9a-47 ◽

2020 ◽

Author(s):

A. I. Lopato ◽

◽

A. G. Eremenko ◽

Keyword(s):

Chemical Kinetics ◽

Numerical Scheme ◽

Unstructured Grids ◽

Numerical Study ◽

Numerical Approach ◽

Detonation Waves ◽

Detailed Chemical Kinetics ◽

Parallel Solver ◽

Further Development ◽

Detailed Chemical

Recently, we developed a numerical approach for the simulation of detonation waves on fully unstructured grids and applied it to the numerical study of the mechanisms of detonation initiation in multifocusing systems. Current work is devoted to further development of our numerical approach, namely, parallelization of the numerical scheme and introduction of more comprehensive detailed chemical kinetics scheme.

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Investigation of the stability of periodic motions in a nonlinear automatic control system based on the fast fourier transform

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2003.1.024 ◽

2003 ◽

Vol 3 ◽

pp. 297-307

Author(s):

V.V. Denisov

Keyword(s):

Fourier Transform ◽

Control System ◽

Automatic Control ◽

Fast Fourier Transform ◽

Automatic Control System ◽

Resonance Phenomenon ◽

Periodic Motions ◽

Multiply Connected ◽

Non Linear ◽

The Stability

An approach to the study of the stability of non-linear multiply connected systems of automatic control by means of a fast Fourier transform and the resonance phenomenon is considered.

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On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

Advances in Difference Equations ◽

10.1186/s13662-020-02982-6 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

N. H. Sweilam ◽

S. M. Al-Mekhlafi ◽

A. O. Albalawi ◽

D. Baleanu

Keyword(s):

Mathematical Model ◽

Optimal Control ◽

Weighted Average ◽

Necessary Optimality Conditions ◽

Numerical Approach ◽

Population Number ◽

Infected People ◽

The Stability ◽

Novel Coronavirus ◽

Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

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A Practical Numerical Approach to Characterizing Non-Linear Shrinkage and Optimizing Dimensional Deviation of Injection-Molded Small Module Plastic Gears

Polymers ◽

10.3390/polym13132092 ◽

2021 ◽

Vol 13 (13) ◽

pp. 2092

Author(s):

Xiansong He ◽

Wangqing Wu

Keyword(s):

Injection Molding ◽

High Speed ◽

Numerical Approach ◽

Linear Shrinkage ◽

Influential Factor ◽

Dimensional Deviation ◽

Non Linear ◽

Injection Molded ◽

Plastic Gears ◽

Circle Diameter

This paper was aimed at finding out the solution to the problem of insufficient dimensional accuracy caused by non-linear shrinkage deformation during injection molding of small module plastic gears. A practical numerical approach was proposed to characterize the non-linear shrinkage and optimize the dimensional deviation of the small module plastic gears. Specifically, Moldflow analysis was applied to visually simulate the shrinkage process of small module plastic gears during injection molding. A 3D shrinkage gear model was obtained and exported to compare with the designed gear model. After analyzing the non-linear shrinkage characteristics, the dimensional deviation of the addendum circle diameter and root circle diameter was investigated by orthogonal experiments. In the end, a high-speed cooling concept for the mold plate and the gear cavity was proposed to optimize the dimensional deviation. It was confirmed that the cooling rate is the most influential factor on the non-linear shrinkage of the injection-molded small module plastic gears. The dimensional deviation of the addendum circle diameter and the root circle diameter can be reduced by 22.79% and 22.99% with the proposed high-speed cooling concept, respectively.

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