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Journal articles on the topic 'Second-order method'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Bradji, Abdallah, and Jürgen Fuhrmann. "Some new error estimates for finite element methods for second order hyperbolic equations using the Newmark method." Mathematica Bohemica 139, no. 2 (2014): 125–36. http://dx.doi.org/10.21136/mb.2014.143843.

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2

Zhao, Yan-Gang, Tetsuro Ono, and Masahiro Kato. "Second-Order Third-Moment Reliability Method." Journal of Structural Engineering 128, no. 8 (August 2002): 1087–90. http://dx.doi.org/10.1061/(asce)0733-9445(2002)128:8(1087).

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3

Lee, Seok, Heung-Jae Lie, Kyu-Min Song, and Chong-Jeanne Lim. "A second-order particle tracking method." Ocean Science Journal 40, no. 4 (December 2005): 201–8. http://dx.doi.org/10.1007/bf03023519.

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4

Qiu, Zhi-Yong, Yao-Lin Jiang, and Jia-Wei Yuan. "Interpolatory Model Order Reduction Method for Second Order Systems." Asian Journal of Control 20, no. 1 (June 5, 2017): 312–22. http://dx.doi.org/10.1002/asjc.1550.

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5

Xie, Zong Wu, Cao Li, and Hong Liu. "Cosine Second Order Robot Trajectory Planning Method." Applied Mechanics and Materials 80-81 (July 2011): 1075–80. http://dx.doi.org/10.4028/www.scientific.net/amm.80-81.1075.

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A new joint space trajectory planning method for the series robot is proposed. Comparing with the traditional path planning methods which can only guarantee the planned trajectory velocity or acceleration continuous, the proposed trajectory planning algorithm can also ensure the derivative of acceleration (Jerk) continuous within a limit threshold. At the end of this paper, the proposed path planning algorithm is validated of having a great performance on robot trajectory tracking.

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6

Liu, Miao, and Bin Wang. "A Web Second-Order Vulnerabilities Detection Method." IEEE Access 6 (2018): 70983–88. http://dx.doi.org/10.1109/access.2018.2881070.

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7

Teng, Zhongming, Linzhang Lu, and Xiaoqian Niu. "Restartable Generalized Second Order Krylov Subspace Method." Journal of Computational and Theoretical Nanoscience 12, no. 11 (November 1, 2015): 4584–92. http://dx.doi.org/10.1166/jctn.2015.4405.

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8

Azarenok, Boris N. "Realization of a second-order Godunov's method." Computer Methods in Applied Mechanics and Engineering 189, no. 3 (September 2000): 1031–52. http://dx.doi.org/10.1016/s0045-7825(00)00194-8.

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9

Corradi, Gianfranco. "A second order method for unconstrained optimization." International Journal of Computer Mathematics 20, no. 3-4 (January 1986): 253–60. http://dx.doi.org/10.1080/00207168608803547.

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10

Wei, Haixin, Ray Luo, and Ruxi Qi. "An efficient second‐order poisson–boltzmann method." Journal of Computational Chemistry 40, no. 12 (February 18, 2019): 1257–69. http://dx.doi.org/10.1002/jcc.25783.

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11

Xia, Yu, and Farid Alizadeh. "The method for second order cone programming." Computers & Operations Research 35, no. 5 (May 2008): 1510–38. http://dx.doi.org/10.1016/j.cor.2006.08.009.

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12

Bousri, Sebti. "A parallel nodal method of second order." Future Generation Computer Systems 11, no. 2 (March 1995): 153–60. http://dx.doi.org/10.1016/0167-739x(95)00056-x.

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13

Goliński, Tomasz, and Anatol Odzijewicz. "Factorization method for second order functional equations." Journal of Computational and Applied Mathematics 176, no. 2 (April 2005): 331–55. http://dx.doi.org/10.1016/j.cam.2004.07.023.

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14

Tuloli, Mohamad Syafri, Benhard Sitohang, and Bayu Hendradjaya. "Coevolution of Second-order-mutant." International Journal of Electrical and Computer Engineering (IJECE) 8, no. 5 (October 1, 2018): 3238. http://dx.doi.org/10.11591/ijece.v8i5.pp3238-3249.

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<span>One of the obstacles that hinder the usage of mutation testing is its impracticality, two main contributors of this are a large number of mutants and a large number of test cases involves in the process. Researcher usually tries to address this problem by optimizing the mutants and the test case separately. In this research, we try to tackle both of optimizing mutant and optimizing test-case simultaneously using a coevolution optimization method. The coevolution optimization method is chosen for the mutation testing problem because the method works by optimizing multiple collections (population) of a solution. This research found that coevolution is better suited for multi-problem optimization than other single population methods (i.e. Genetic Algorithm), we also propose new indicator to determine the optimal coevolution cycle. The experiment is done to the artificial case, laboratory, and also a real case.</span>

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15

Duan, W. Y., J. K. Chen, and B. B. Zhao. "Second-order Taylor expansion boundary element method for the second-order wave radiation problem." Applied Ocean Research 52 (August 2015): 12–26. http://dx.doi.org/10.1016/j.apor.2015.04.011.

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16

Duan, Wenyang, Jikang Chen, and Binbin Zhao. "Second-order Taylor Expansion Boundary Element Method for the second-order wave diffraction problem." Engineering Analysis with Boundary Elements 58 (September 2015): 140–50. http://dx.doi.org/10.1016/j.enganabound.2015.04.008.

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17

D??ster, A., E. Rank, S. Diebels, T. Ebinger, and H. Steeb. "Second order homogenization method based on higher order finite elements." PAMM 5, no. 1 (December 2005): 391–92. http://dx.doi.org/10.1002/pamm.200510172.

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18

Yuan, Si, Kangsheng Ye, and F. W. Williams. "Second order mode-finding method in dynamic stiffness matrix methods." Journal of Sound and Vibration 269, no. 3-5 (January 2004): 689–708. http://dx.doi.org/10.1016/s0022-460x(03)00126-3.

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19

Cropp, Roger A., and Roger D. Braddock. "The New Morris Method: an efficient second-order screening method." Reliability Engineering & System Safety 78, no. 1 (October 2002): 77–83. http://dx.doi.org/10.1016/s0951-8320(02)00109-6.

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20

Bai, Zhaojun, and Yangfeng Su. "Dimension Reduction of Large-Scale Second-Order Dynamical Systems via a Second-Order Arnoldi Method." SIAM Journal on Scientific Computing 26, no. 5 (January 2005): 1692–709. http://dx.doi.org/10.1137/040605552.

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21

Antczak, Tadeusz. "A second order η-approximation method for constrained optimization problems involving second order invex functions." Applications of Mathematics 54, no. 5 (September 12, 2009): 433–45. http://dx.doi.org/10.1007/s10492-009-0028-2.

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22

Lin, Yiqin, Liang Bao, and Yimin Wei. "Model-order reduction of large-scale second-order MIMO dynamical systems via a block second-order Arnoldi method." International Journal of Computer Mathematics 84, no. 7 (July 2007): 1003–19. http://dx.doi.org/10.1080/00207160701253836.

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23

Ibrahim, Zarina Bibi, Nooraini Zainuddin, Khairil Iskandar Othman, Mohamed Suleiman, and Iskandar Shah Mohd Zawawi. "Variable Order Block Method for Solving Second Order Ordinary Differential Equations." Sains Malaysiana 48, no. 8 (August 31, 2019): 1761–69. http://dx.doi.org/10.17576/jsm-2019-4808-23.

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24

Xin, Zhenfang, Zhengxing Zuo, Huihua Feng, David Wagg, and Simon Neild. "Higher order accuracy analysis of the second-order normal form method." Nonlinear Dynamics 70, no. 3 (September 26, 2012): 2175–85. http://dx.doi.org/10.1007/s11071-012-0608-7.

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25

Chen, Jiu, Ming Qian Wang, Xin Zhou, Ling Yang, Wei-Qi Li, and Wei Quan Tian. "Two-dimensional second-order nonlinear optical spectra: landscape of second-order nonlinear optics." Physical Chemistry Chemical Physics 19, no. 43 (2017): 29315–20. http://dx.doi.org/10.1039/c7cp05910h.

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26

Rama Mohana Rao, K. "Second-order piezomagnetism in polychromatic crystals." Acta Crystallographica Section A Foundations of Crystallography 46, no. 2 (February 1, 1990): 130–33. http://dx.doi.org/10.1107/s0108767389010664.

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The group-theoretical method established for obtaining the non-vanishing independent number of constants required to describe a magnetic/physical property in respect of the 18 polychromatic crystal classes [Rama Mohana Rao (1987). J. Phys. A, 20, 47-57] has been explored to enumerate the second- order piezomagnetic coefficients (n i ′) for the same classes. The advantage of Jahn's method [Jahn (1949). Acta Cryst. 2, 30-33] is appreciated in obtaining these n i ′ through the reduction of a representation. The different group-theoretical methods are illustrated with the help of the point group 4. The results obtained for all 18 classes are tabulated and briefly discussed.

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27

Toma, Cristian. "Filtering Method Based on Symmetrical Second Order Systems." Symmetry 11, no. 6 (June 20, 2019): 813. http://dx.doi.org/10.3390/sym11060813.

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This study presents a filtering and sampling structure based on symmetrical second order systems working on half-period. It is shown that undamped second order oscillating systems working on half-period could provide: (i) a large attenuation coefficient for an alternating signal (due to the filtering second order system), and (ii) a robust sampling procedure (the slope of the generated output being zero at the sampling time moment). Unlike previous studies on the same topics, these results are achieved without the use of an additional integrator.

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28

Sindu Devi, S., and K. Ganesan. "Fuzzy picard’s method for derivatives of second order." Journal of Physics: Conference Series 1000 (April 2018): 012038. http://dx.doi.org/10.1088/1742-6596/1000/1/012038.

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29

Abed-Meraim, K., E. Moulines, and P. Loubaton. "Prediction error method for second-order blind identification." IEEE Transactions on Signal Processing 45, no. 3 (March 1997): 694–705. http://dx.doi.org/10.1109/78.558487.

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30

Awawdeh, Fadi. "Perturbation method for abstract second-order inverse problems." Nonlinear Analysis: Theory, Methods & Applications 72, no. 3-4 (February 2010): 1379–86. http://dx.doi.org/10.1016/j.na.2009.08.021.

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31

Lu, Zhao-Hui, Dong-Zhu Hu, and Yan-Gang Zhao. "Second-Order Fourth-Moment Method for Structural Reliability." Journal of Engineering Mechanics 143, no. 4 (April 2017): 06016010. http://dx.doi.org/10.1061/(asce)em.1943-7889.0001199.

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32

Alotto, Piergiorgio, and Fabio Freschi. "A Second-Order Cell Method for Poisson's Equation." IEEE Transactions on Magnetics 47, no. 5 (May 2011): 1430–33. http://dx.doi.org/10.1109/tmag.2010.2092419.

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33

Tabak, Esteban G. "A Second-Order Godunov Method on Arbitrary Grids." Journal of Computational Physics 124, no. 2 (March 1996): 383–95. http://dx.doi.org/10.1006/jcph.1996.0067.

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34

MATSUMOTO, Kazuhisa, Toshikazu TAKEDA, and Tomoaki MASUDA. "Approximate Calculation Method for Second Order Sensitivity Coefficient." Journal of Nuclear Science and Technology 31, no. 11 (November 1994): 1151–59. http://dx.doi.org/10.1080/18811248.1994.9735272.

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35

Zhao, Yang. "A Second Order IMEX Method for Radiation Hydrodynamics." Journal of Physics: Conference Series 1600 (July 2020): 012064. http://dx.doi.org/10.1088/1742-6596/1600/1/012064.

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36

Helmberg, C., M. L. Overton, and F. Rendl. "The spectral bundle method with second-order information." Optimization Methods and Software 29, no. 4 (February 7, 2014): 855–76. http://dx.doi.org/10.1080/10556788.2013.858155.

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37

Bouchitté, Guy, Ilaria Fragalà, and Ilaria Lucardesi. "A Variational Method for Second Order Shape Derivatives." SIAM Journal on Control and Optimization 54, no. 2 (January 2016): 1056–84. http://dx.doi.org/10.1137/15100494x.

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38

Goto, Y., and N. Fujii. "Second-order numerical method for domain optimization problems." Journal of Optimization Theory and Applications 67, no. 3 (December 1990): 533–50. http://dx.doi.org/10.1007/bf00939648.

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39

Huang, Xianzhen, Yuxiong Li, Yimin Zhang, and Xufang Zhang. "A new direct second-order reliability analysis method." Applied Mathematical Modelling 55 (March 2018): 68–80. http://dx.doi.org/10.1016/j.apm.2017.10.026.

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40

Rasina, I. V., and O. V. Danilenko. "Second Order Krotov Method for Discrete-Continuous Systems." Bulletin of Irkutsk State University. Series Mathematics 32 (2020): 17–32. http://dx.doi.org/10.26516/1997-7670.2020.32.17.

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41

Yousefi, Hassan, Seyed Shahram Ghorashi, and Timon Rabczuk. "Directly Simulation of Second Order Hyperbolic Systems in Second Order Form via the Regularization Concept." Communications in Computational Physics 20, no. 1 (June 22, 2016): 86–135. http://dx.doi.org/10.4208/cicp.101214.011015a.

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AbstractWe present an efficient and robust method for stress wave propagation problems (second order hyperbolic systems) having discontinuities directly in their second order form. Due to the numerical dispersion around discontinuities and lack of the inherent dissipation in hyperbolic systems, proper simulation of such problems are challenging. The proposed idea is to denoise spurious oscillations by a post-processing stage from solutions obtained from higher-order grid-based methods (e.g., high-order collocation or finite-difference schemes). The denoising is done so that the solutions remain higher-order (here, second order) around discontinuities and are still free from spurious oscillations. For this purpose, improved Tikhonov regularization approach is advised. This means to let data themselves select proper denoised solutions (since there is no pre-assumptions about regularized results). The improved approach can directly be done on uniform or non-uniform sampled data in a way that the regularized results maintenance continuous derivatives up to some desired order. It is shown how to improve the smoothing method so that it remains conservative and has local estimating feature. To confirm effectiveness of the proposed approach, finally, some one and two dimensional examples will be provided. It will be shown how both the numerical (artificial) dispersion and dissipation can be controlled around discontinuous solutions and stochastic-like results.

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42

Zhang, Guoshan, and Peizhao Yu. "Lyapunov method for stability of descriptor second-order and high-order systems." Journal of Industrial & Management Optimization 14, no. 2 (2018): 673–86. http://dx.doi.org/10.3934/jimo.2017068.

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43

Tirmizi, S. I. A., and E. H. Twizell. "A fourth order multiderivative method for linear second order boundary value problems." International Journal of Computer Mathematics 20, no. 2 (January 1986): 145–55. http://dx.doi.org/10.1080/00207168608803539.

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44

Guha, Paramita, and Mashuq un Nabi. "Reduced Order Modeling of a Microgripper Using SVD-Second-Order Krylov Method." International Journal for Computational Methods in Engineering Science and Mechanics 16, no. 2 (March 4, 2015): 65–70. http://dx.doi.org/10.1080/15502287.2015.1009576.

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45

Lü, Shujuan, Tao Xu, and Zhaosheng Feng. "A second-order numerical method for space–time variable-order diffusion equation." Journal of Computational and Applied Mathematics 389 (June 2021): 113358. http://dx.doi.org/10.1016/j.cam.2020.113358.

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46

Rymarczyk, T., and J. Sikora. "Comparison second order versus zero order boundary element method for tomography imaging." Journal of Physics: Conference Series 1782, no. 1 (February 1, 2021): 012031. http://dx.doi.org/10.1088/1742-6596/1782/1/012031.

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47

Nygaard, Cecilie R., and Jeppe Olsen. "A second-order unconstrained optimization method for canonical-ensemble density-functional methods." Journal of Chemical Physics 138, no. 9 (March 7, 2013): 094109. http://dx.doi.org/10.1063/1.4791571.

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48

Shimada, Masao, David Tae, Tao Xue, Rohit Deokar, and K. K. Tamma. "Second order accurate particle-based formulations." International Journal of Numerical Methods for Heat & Fluid Flow 26, no. 3/4 (May 3, 2016): 897–915. http://dx.doi.org/10.1108/hff-10-2015-0424.

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Purpose – The purpose of this paper is to present new implementation aspects of unified explicit time integration algorithms, called the explicit GS4-II family of algorithms, of a second-order time accuracy in all the unknowns (e.g. positions, velocities, and accelerations) with particular attention to the moving-particle simulation (MPS) method for solving the incompressible fluids with free surfaces. Design/methodology/approach – In the present paper, the explicit GS4-II family of algorithms is implemented in the MPS method in the following two different approaches: a direct explicit formulation with the use of the weak incompressibility equation involving the (modified) speed of sound; and a predictor-corrector explicit formulation. The first approach basically follows the concept of the explicit MPS method, presented in the literature, and the latter approach employs a similar concept used in, for example, a fractional-step method in computational fluid dynamics. Findings – Illustrative numerical examples demonstrate that any scheme within the proposed algorithmic framework captures the physics with the necessary second-order time accuracy and stability. Originality/value – The new algorithmic framework extended with the GS4-II family encompasses a multitude of pastand new schemes and offers a general purpose and unified implementation.

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49

Liang, Zhizheng. "Feature Scaling via Second-Order Cone Programming." Mathematical Problems in Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/7347986.

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Feature scaling has attracted considerable attention during the past several decades because of its important role in feature selection. In this paper, a novel algorithm for learning scaling factors of features is proposed. It first assigns a nonnegative scaling factor to each feature of data and then adopts a generalized performance measure to learn the optimal scaling factors. It is of interest to note that the proposed model can be transformed into a convex optimization problem: second-order cone programming (SOCP). Thus the scaling factors of features in our method are globally optimal in some sense. Several experiments on simulated data, UCI data sets, and the gene data set are conducted to demonstrate that the proposed method is more effective than previous methods.

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50

Nhat, L. A. "Pseudospectral method for second-order autonomous nonlinear differential equations." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 29, no. 1 (March 2019): 61–72. http://dx.doi.org/10.20537/vm190106.

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