scholarly journals Five Ways of Reducing the Crank-Nicolson Oscillations

2002 ◽  
Vol 31 (558) ◽  
Author(s):  
Ole Østerby
Keyword(s):  
Parabolic Equations ◽  
Initial Conditions ◽  
Second Order ◽  
Unconditionally Stable ◽  
Popular Method ◽  
Jump Discontinuities ◽  
Long Time ◽  
Selection Of ◽  
Crank Nicolson

Crank-Nicolson is a popular method for solving parabolic equations because it is unconditionally stable and second order accurate. One drawback of CN is that it responds to jump discontinuities in the initial conditions with oscillations which are weakly damped and therefore may persist for a long time. We present a selection of methods to reduce the amplitude of these oscillations.

SISTEM PENDUKUNG KEPUTUSAN PEMILIHAN KEPALA CABANG TERBAIK BANK SUMUT DENGAN MENERAPKAN METODE VIKOR

2018 ◽  
Vol 2 (1) ◽  
Author(s):  
Betrik J Hutapea ◽  
Mesran Mesran ◽  
Siti Nurhabibah
Keyword(s):  
Decision Support ◽  
Decision Support System ◽  
Support System ◽  
Development Bank ◽  
Vikor Method ◽  
The North ◽  
Long Time ◽  
North Sumatra ◽  
Regional Development Bank ◽  
Selection Of

SUMUT Bank is one of the Banks in Indonesia with the name of the company PT. Regional Development Bank of North Sumatra. The North Sumatra Bank has branches in each region in North Sumatra both in the district and in the sub-district, and each of these branches is led by a branch leader or branch head. The head of this branch is responsible for the reversal of the Bank being led. The best and most accomplished branch heads deserve more and more awards. The selection of the best branch heads is selected transparently and structured in the hope that it can be a motivation for all branch heads to be able to further improve the quality and service of the Bank they lead. Making the best branch head selection done manually will take a long time and tends to be less transparent and structured. One solution so that the implementation of the selection can be carried out easily and quickly, it requires a Decision Support System that can provide consistency of assessment. In this study the method used is the VIKOR method (Visekriterijumsko Kompromisno Rangiranje). This method makes cracking on alternatives based on criteria that have been determined with an ideal compromise solution or the best solution, so that this system can later be beneficial for the SUMUT Bank to get the title in determining the best branch head.Keywords: Decision Support System, North Sumatra Bank, Branch Head, Vikor

Numerical analysis of trajectories in a Cassinian ion trap of second order with trap door ion inlet

2021 ◽  
Vol 27 (1) ◽  
pp. 3-12
Author(s):  
Bjoern Raupers ◽  
Hana Medhat ◽  
Juergen Grotemeyer ◽  
Frank Gunzer
Keyword(s):  
Ion Trap ◽  
Ion Traps ◽  
Second Order ◽  
Resolving Power ◽  
Periodic Pattern ◽  
Ion Motion ◽  
Trap Door ◽  
Mass Resolving Power ◽  
Long Time ◽  
The Fourier Transform

Ion traps like the Orbitrap are well known mass analyzers with very high resolving power. This resolving power is achieved with help of ions orbiting around an inner electrode for long time, in general up to a few seconds, since the mass signal is obtained by calculating the Fourier Transform of the induced signal caused by the ion motion. A similar principle is applied in the Cassinian Ion Trap of second order, where the ions move in a periodic pattern in-between two inner electrodes. The Cassinian ion trap has the potential to offer mass resolving power comparable to the Orbitrap with advantages regarding the experimental implementation. In this paper we have investigated the details of the ion motion analyzing experimental data and the results of different numerical methods, with focus on increasing the resolving power by increasing the oscillation frequency for ions in a high field ion trap. In this context the influence of the trap door, a tunnel through which the ions are injected into the trap, on the ion velocity becomes especially important.

scholarly journals Internet page content analysis of north European Sea ports

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Olli-Pekka Hilmola ◽  
Andres Tolli ◽  
Ain Kiisler
Keyword(s):  
Content Analysis ◽  
Environmental Issues ◽  
Basic Design ◽  
Time Period ◽  
Long Time ◽  
Sea Ports ◽  
Selection Of

Abstract This study analyses 98 Internet pages of sea ports located in Sweden, Finland and Estonia during years 2017–2019. Aim of the study is to find, how website basic design is completed (colours and languages), how slogans, environmental issues, statistics and hinterland transports are reported. Based on the analysis, it appears as rather common that sea ports follow conservative selection of colours in their websites, where blue and white are clearly most popular. Typically, English and Swedish are as the most common used language, followed by Finnish, Russian and Estonian. In some rare cases, websites are offered in Chinese or German. Larger sea ports do have clear “slogans”, where smaller ones are just having lengthy justification for their existence. Environmental issues are increasing concern among sea ports, and these are mostly mentioned in details within Swedish actors. Providing statistics varies among companies, and in some sea ports these are provided from very long time period, where in others from just previous years or then only from last year (or even at all). It is common for companies to report that they have sustainable hinterland access, railway available.

scholarly journals Verification of Convergence Rates of Numerical Solutions for Parabolic Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Darae Jeong ◽  
Yibao Li ◽  
Chaeyoung Lee ◽  
Junxiang Yang ◽  
Yongho Choi ◽  
...  
Keyword(s):  
Parabolic Equations ◽  
Convergence Rates ◽  
Numerical Solutions ◽  
Second Order ◽  
Order Convergence ◽  
Numerical Convergence ◽  
Verification Method ◽  
First Order ◽  
Convergence Test ◽  
Second Order Convergence

In this paper, we propose a verification method for the convergence rates of the numerical solutions for parabolic equations. Specifically, we consider the numerical convergence rates of the heat equation, the Allen–Cahn equation, and the Cahn–Hilliard equation. Convergence test results show that if we refine the spatial and temporal steps at the same time, then we have the second-order convergence rate for the second-order scheme. However, in the case of the first-order in time and the second-order in space scheme, we may have the first-order or the second-order convergence rates depending on starting spatial and temporal step sizes. Therefore, for a rigorous numerical convergence test, we need to perform the spatial and the temporal convergence tests separately.

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