Two-Step Method

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Nikos Chatzigrigoriou - One of the best experts on this subject based on the ideXlab platform.

  • Thermoplastic Elastomers.pdf
    internal, 2017
    Co-Authors: Nikos Chatzigrigoriou
    Abstract:

    phase. 5.2 Two-step methods TPU can be synthesised by a two-step method, which is known as prepolymer method. The reaction may be carried out in two steps … . The structural regularity leads to a better packing of hard segments where physical cross-linking points are easier to form. Hence, a two-step method gives

T. E. Simos - One of the best experts on this subject based on the ideXlab platform.

  • New hybrid Two-Step Method with optimized phase and stability characteristics
    Journal of Mathematical Chemistry, 2018
    Co-Authors: V. N. Kovalnogov, R. V. Fedorov, A. A. Bondarenko, T. E. Simos
    Abstract:

    In this paper and for the first time in the literature, we develop a new Runge–Kutta type symmetric Two-Step finite difference pair with the following characteristics: the new algorithm is of symmetric type, the new algorithm is of Two-Step, the new algorithm is of five-stages, the new algorithm is of twelfth-algebraic order, the new algorithm is based on the following approximations: 1. the first layer on the point $$x_{n-1}$$ x n - 1 , 2. the second layer on the point $$x_{n-1}$$ x n - 1 , 3. the third layer on the point $$x_{n-1}$$ x n - 1 , 4. the fourth layer on the point $$x_{n}$$ x n and finally, 5. the fifth (final) layer on the point $$x_{n+1}$$ x n + 1 , the new algorithm has vanished the phase-lag and its first, second, third and fourth derivatives, the new algorithm has improved stability characteristics for the general problems, the new algorithm is of P-stable type since it has an interval of periodicity equal to $$\left( 0, \infty \right) $$ 0 , ∞ . For the new developed algorithm we present a detailed numerical analysis (local truncation error and stability analysis). The effectiveness of the new developed algorithm is evaluated with the approximate solution of coupled differential equations arising from the Schrödinger type.

  • New five-stages Two-Step Method with improved characteristics
    Journal of Mathematical Chemistry, 2018
    Co-Authors: Junfeng Yao, T. E. Simos
    Abstract:

    In the present paper and for the first time in the literature, a new five-stages symmetric Two-Step Method with improved characteristics is developed.

  • a new two stage symmetric two step Method with vanished phase lag and its first second third and fourth derivatives for the numerical solution of the radial schrodinger equation
    Journal of Mathematical Chemistry, 2016
    Co-Authors: Zhou Zhou, T. E. Simos
    Abstract:

    A two stage symmetric Two-Step Method with vanished phase-lag and its first, second, third and fourth derivatives with low computational cost is developed in this paper for the first time in the literature. More specifically in this paper we present: the theoretical background for the development of the new low computational and high efficient Method, the development of the Method, the local truncation error analysis based on the radial Schrodinger equation, the interval of periodicity—stability analysis, the examination of the efficiency of the new produced Method by applying it to the numerical solution of the Schrodinger equation.

  • a runge kutta type implicit high algebraic order two step Method with vanished phase lag and its first second third and fourth derivatives for the numerical solution of coupled differential equations arising from the schrodinger equation
    Journal of Mathematical Chemistry, 2015
    Co-Authors: Kenan Mu, T. E. Simos
    Abstract:

    A Runge–Kutta type (four stages) eighth algebraic order Two-Step Method with phase-lag and its first, second, third and fourth derivatives equal to zero is produced in this paper. We also study the results of elimination of the phase-lag and its derivatives on the efficiency of the Method. Our studies consist: (1) the construction of the Method, (2) the determination of the local truncation error of the proposed Method, (3) the investigation of the local truncation error analysis using the comparison with other similar Methods of the literature, (4) the computation of the interval of periodicity (stability interval) of the developed Method. For this calculation we use a scalar test equation with frequency different than the frequency of the scalar test equation used for the phase-lag analysis, (5) the definition of the error estimation based on Methods with different algebraic orders and (6) the investigation of the effectiveness of the new obtained Method studying the numerical solution of the coupled differential equations arising from the Schrodinger equation.

  • A Two-Step Method for the numerical solution of the radial Schrödinger equation
    Computers & Mathematics with Applications, 1995
    Co-Authors: T. E. Simos, G. Mousadis
    Abstract:

    Abstract A Two-Step Method is developed for the numerical solution of the radial Schrodinger equation. Numerical results obtained for the integration of resonance problem and eigenvalue problem show that this new Method is better than other similar Methods.

Willem Van Jaarsveld - One of the best experts on this subject based on the ideXlab platform.

  • A Two-Step Method for forecasting spare parts demand using information on component repairs
    European Journal of Operational Research, 2012
    Co-Authors: Ward Romeijnders, Ruud H. Teunter, Willem Van Jaarsveld
    Abstract:

    Abstract Forecasting spare parts demand is notoriously difficult, as demand is typically intermittent and lumpy. Specialized Methods such as that by Croston are available, but these are not based on the repair operations that cause the intermittency and lumpiness of demand. In this paper, we do propose a Method that, in addition to the demand for spare parts, considers the type of component repaired. This Two-Step forecasting Method separately updates the average number of parts needed per repair and the number of repairs for each type of component. The Method is tested in an empirical, comparative study for a service provider in the aviation industry. Our results show that the Two-Step Method is one of the most accurate Methods, and that it performs considerably better than Croston’s Method. Moreover, contrary to other Methods, the Two-Step Method can use information on planned maintenance and repair operations to reduce forecasts errors by up to 20%. We derive further analytical and simulation results that help explain the empirical findings.

Ward Romeijnders - One of the best experts on this subject based on the ideXlab platform.

  • A Two-Step Method for forecasting spare parts demand using information on component repairs
    European Journal of Operational Research, 2012
    Co-Authors: Ward Romeijnders, Ruud H. Teunter, Willem Van Jaarsveld
    Abstract:

    Abstract Forecasting spare parts demand is notoriously difficult, as demand is typically intermittent and lumpy. Specialized Methods such as that by Croston are available, but these are not based on the repair operations that cause the intermittency and lumpiness of demand. In this paper, we do propose a Method that, in addition to the demand for spare parts, considers the type of component repaired. This Two-Step forecasting Method separately updates the average number of parts needed per repair and the number of repairs for each type of component. The Method is tested in an empirical, comparative study for a service provider in the aviation industry. Our results show that the Two-Step Method is one of the most accurate Methods, and that it performs considerably better than Croston’s Method. Moreover, contrary to other Methods, the Two-Step Method can use information on planned maintenance and repair operations to reduce forecasts errors by up to 20%. We derive further analytical and simulation results that help explain the empirical findings.

Xiao Qin Pan - One of the best experts on this subject based on the ideXlab platform.

  • microstructural optical and electrical properties of sno thin films prepared on quartz via a two step Method
    ACS Applied Materials & Interfaces, 2010
    Co-Authors: Lingyan Liang, Zhimin Liu, Hongtao Cao, Xiao Qin Pan
    Abstract:

    A simple, cost-effective, Two-Step Method was proposed for preparing single-phase SnO polycrystalline thin films on quartz. X-ray diffraction (XRD) analysis demonstrated that the annealed films were consisted of polycrystalline α-SnO phase without preferred orientation, and chemical composition analysis of the single phase in nature was analyzed using X-ray photoelectron spectroscopy (XPS). Transmittance spectra in UV−vis−IR range indicated that the average transmittance of both the as-deposited and the annealed SnO thin films was up to 70%. The optical band gap decreased from 3.20 to 2.77 eV after the annealing process, which was attributed to the crystalline size related quantum size effect. Photoluminescence (PL) spectrum of the annealed film showed only a weak peak at 585 nm, and no intrinsic optical transition emission was observed. Moreover, the p-type conductivity of SnO film was confirmed through Hall effect measurement, with Hall mobility of 1.4 cm2 V−1 s−1 and hole concentration of 2.8 × 1016 cm−3.