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Journal articles on the topic 'Higher Order Method'

Author: Grafiati

Published: 6 September 2023

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1

You-zhong, Guo, Liu Zeng-rong, Jiang Xia-mei, and Han Zhi-bin. "Higher-order Melnikov method." Applied Mathematics and Mechanics 12, no. 1 (January 1991): 21–32. http://dx.doi.org/10.1007/bf02018063.

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2

Chin, Wei-Ngan, and John Darlington. "A higher-order removal method." Lisp and Symbolic Computation 9, no. 4 (December 1996): 287–322. http://dx.doi.org/10.1007/bf01806315.

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3

Amat, Sergio, and Sonia Busquier. "On a higher order Secant method." Applied Mathematics and Computation 141, no. 2-3 (September 2003): 321–29. http://dx.doi.org/10.1016/s0096-3003(02)00257-6.

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4

Kim, Oleksiy S., and Peter Meincke. "Adaptive Integral Method for Higher Order Method of Moments." IEEE Transactions on Antennas and Propagation 56, no. 8 (August 2008): 2298–305. http://dx.doi.org/10.1109/tap.2008.926759.

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5

A. Ashour, Ola. "Basic Steffensen's Method of Higher-Order Convergence." International Journal of Advanced Engineering Research and Science 8, no. 4 (2021): 184–91. http://dx.doi.org/10.22161/ijaers.84.22.

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6

Seong Keun Yi and 변경희. "Higher Order Quantification Method for PLS Correlation." Journal of Product Research 29, no. 3 (May 2011): 143–49. http://dx.doi.org/10.36345/kacst.2011.29.3.013.

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7

Keierleber, C. W., and B. T. Rosson. "Higher-Order Implicit Dynamic Time Integration Method." Journal of Structural Engineering 131, no. 8 (August 2005): 1267–76. http://dx.doi.org/10.1061/(asce)0733-9445(2005)131:8(1267).

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8

Chen, Ji, Zhu Wang, and Yinchao Chen. "Higher-order alternative direction implicit FDTD method." Electronics Letters 38, no. 22 (2002): 1321. http://dx.doi.org/10.1049/el:20020911.

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9

Fu, W., and E. L. Tan. "Compact higher-order split-step FDTD method." Electronics Letters 41, no. 7 (2005): 397. http://dx.doi.org/10.1049/el:20057927.

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10

Shim, Hyungseop. "Higher-order α-method in computational plasticity." KSCE Journal of Civil Engineering 9, no. 3 (May 2005): 255–59. http://dx.doi.org/10.1007/bf02829054.

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11

Bykov, Yu. "Higher order numerical method for aeroelastic problems." Journal of Mechanical Engineering 21, no. 1 (March 31, 2018): 11–18. http://dx.doi.org/10.15407/pmach2018.01.011.

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12

Sarangan, A. M., and Wei-Ping Huang. "A higher order electron wave propagation method." IEEE Journal of Quantum Electronics 31, no. 6 (June 1995): 1107–13. http://dx.doi.org/10.1109/3.387049.

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13

Zhang, Qinghui, Uday Banerjee, and Ivo Babuška. "Higher order stable generalized finite element method." Numerische Mathematik 128, no. 1 (January 18, 2014): 1–29. http://dx.doi.org/10.1007/s00211-014-0609-1.

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14

Lee, C. L., and C. T. Lee. "A HIGHER ORDER METHOD OF MULTIPLE SCALES." Journal of Sound and Vibration 202, no. 2 (May 1997): 284–87. http://dx.doi.org/10.1006/jsvi.1996.0736.

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15

Omerović, Samir, and Thomas-Peter Fries. "Higher-order conformal decomposition finite element method." PAMM 16, no. 1 (October 2016): 855–56. http://dx.doi.org/10.1002/pamm.201610416.

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16

Olesen, K., B. Gervang, J. N. Reddy, and M. Gerritsma. "A higher-order equilibrium finite element method." International Journal for Numerical Methods in Engineering 114, no. 12 (February 28, 2018): 1262–90. http://dx.doi.org/10.1002/nme.5785.

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17

Fu, Weiming, and Eng Leong Tan. "A compact higher-order ADI-FDTD method." Microwave and Optical Technology Letters 44, no. 3 (2004): 273–75. http://dx.doi.org/10.1002/mop.20609.

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18

González, David, Elías Cueto, and Manuel Doblaré. "Higher‐order natural element methods: Towards an isogeometric meshless method." International Journal for Numerical Methods in Engineering 74, no. 13 (June 25, 2008): 1928–54. http://dx.doi.org/10.1002/nme.2237.

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19

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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20

Chen, Jeng-Ming, and Bor-Sen Chen. "A higher-order correlation method for model-order and parameter estimation." Automatica 30, no. 8 (August 1994): 1339–44. http://dx.doi.org/10.1016/0005-1098(94)90113-9.

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21

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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22

SUZUKI, Kohji, Isao KIMPARA, and Kazuro KAGEYAMA. "Leyerwise Higher-Order Finite Element with Penalty Method." Journal of the Japan Society for Composite Materials 25, no. 3 (1999): 109–19. http://dx.doi.org/10.6089/jscm.25.109.

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23

Nonaka, Andrew, David Trebotich, Gregory Miller, Daniel Graves, and Phillip Colella. "A higher-order upwind method for viscoelastic flow." Communications in Applied Mathematics and Computational Science 4, no. 1 (June 11, 2009): 57–83. http://dx.doi.org/10.2140/camcos.2009.4.57.

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24

Moysi, Alejandro, Ioannis K. Argyros, Samundra Regmi, Daniel González, Á. Alberto Magreñán, and Juan Antonio Sicilia. "Convergence and Dynamics of a Higher-Order Method." Symmetry 12, no. 3 (March 5, 2020): 420. http://dx.doi.org/10.3390/sym12030420.

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Solving problems in various disciplines such as biology, chemistry, economics, medicine, physics, and engineering, to mention a few, reduces to solving an equation. Its solution is one of the greatest challenges. It involves some iterative method generating a sequence approximating the solution. That is why, in this work, we analyze the convergence in a local form for an iterative method with a high order to find the solution of a nonlinear equation. We extend the applicability of previous results using only the first derivative that actually appears in the method. This is in contrast to either works using a derivative higher than one, or ones not in this method. Moreover, we consider the dynamics of some members of the family in order to see the existing differences between them.

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25

Han, Feng, Zheng Liang Li, and Wen Liang Fan. "A New Adaptive Higher Order Response Surface Method." Advanced Materials Research 243-249 (May 2011): 5946–54. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.5946.

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Response surface method has won numerous concerns in the reliability analysis of structure due to its simplicity and practicability, especially quadratic response surface taking no account of cross terms is most widely used. However, for the complex ultimate state curved surface corresponding to strongly nonlinear, the approximate accuracy of quadratic response surface is apparently not enough, causing a biggish error in estimation of reliability. Although, theoretically, higher order response surface method can resolve this problem, the sharp increase of undetermined coefficient reduces calculation efficiency, and even, cannot achieve. Therefore, on the basis of univariate analysis of multivariable function, an algorithm which can reasonably determine higher order response surface form is presented in this article, able to effectively reduce the number of undetermined coefficients in response surface, so as to reduce computational difficulties and put forward improving measures for possible problems; In addition, based on the tactics of number-theoretic setpoint, a type of scheme of number-theoretic selecting point applicable to response surface method has been developed. Finally, through the analysis of examples, the suggested algorithm was validated, with the result showing that the algorithm has good accuracy and efficiency.

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26

Jiang, Ying, Si Li, and Yuesheng Xu. "A Higher-Order Polynomial Method for SPECT Reconstruction." IEEE Transactions on Medical Imaging 38, no. 5 (May 2019): 1271–83. http://dx.doi.org/10.1109/tmi.2018.2881919.

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27

NISHIO, Shigeru, Taketoshi OKUNO, and Shusaku MORIKAWA. "Higher Order Approximation for Spatio-Temporal Derivative Method." Journal of the Visualization Society of Japan 12, no. 1Supplement (1992): 127–30. http://dx.doi.org/10.3154/jvs.12.1supplement_127.

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28

Beltrametti, M., P. Francia, and A. J. Sommese. "On Reider?s method and higher order embeddings." Duke Mathematical Journal 58, no. 2 (April 1989): 425–39. http://dx.doi.org/10.1215/s0012-7094-89-05819-5.

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29

Sung-Taek Chun and J. Y. Choe. "A higher order FDTD method in Integral formulation." IEEE Transactions on Antennas and Propagation 53, no. 7 (July 2005): 2237–46. http://dx.doi.org/10.1109/tap.2005.850708.

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30

Trif, Damian. "Operatorial Tau Method for Higher Order Differential Problems." British Journal of Mathematics & Computer Science 3, no. 4 (January 10, 2013): 772–93. http://dx.doi.org/10.9734/bjmcs/2013/5232.

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31

Yang, Zhong-Hua, and H. B. Keller. "A Direct Method for Computing Higher Order Folds." SIAM Journal on Scientific and Statistical Computing 7, no. 2 (April 1986): 351–61. http://dx.doi.org/10.1137/0907024.

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32

Kirchner, E., and B. Simeon. "A higher-order time integration method for viscoplasticity." Computer Methods in Applied Mechanics and Engineering 175, no. 1-2 (June 1999): 1–18. http://dx.doi.org/10.1016/s0045-7825(98)00369-7.

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33

Vulanović, Relja. "A higher-order method for stationary shock problems." Applied Mathematics and Computation 108, no. 2-3 (February 2000): 139–52. http://dx.doi.org/10.1016/s0096-3003(99)00011-9.

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34

Birkelbach, Felix, Markus Deutsch, Stylianos Flegkas, Winter Franz, and Andreas Werner. "A higher-order generalization of the NPK-method." Thermochimica Acta 661 (March 2018): 27–33. http://dx.doi.org/10.1016/j.tca.2018.01.005.

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35

Yamamoto, Toshihiro. "Higher order mode analyses in Feynman-α method." Annals of Nuclear Energy 38, no. 6 (June 2011): 1231–37. http://dx.doi.org/10.1016/j.anucene.2011.02.017.

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36

Borries, Oscar, Peter Meincke, Erik Jorgensen, and Per Christian Hansen. "Multilevel Fast Multipole Method for Higher Order Discretizations." IEEE Transactions on Antennas and Propagation 62, no. 9 (September 2014): 4695–705. http://dx.doi.org/10.1109/tap.2014.2330582.

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37

Bourennane, Salah. "Localization method based on the higher‐order statistics." Journal of the Acoustical Society of America 107, no. 5 (May 2000): 2867. http://dx.doi.org/10.1121/1.429298.

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38

Oger, G., M. Doring, B. Alessandrini, and P. Ferrant. "An improved SPH method: Towards higher order convergence." Journal of Computational Physics 225, no. 2 (August 2007): 1472–92. http://dx.doi.org/10.1016/j.jcp.2007.01.039.

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39

Van de Velde, Antoine, and Robert Beauwens. "A higher order hexagonal-z nodal transport method." Transport Theory and Statistical Physics 24, no. 1-3 (January 1995): 133–54. http://dx.doi.org/10.1080/00411459508205123.

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40

Geiser, Jürgen. "Higher-Order Splitting Method for Elastic Wave Propagation." International Journal of Mathematics and Mathematical Sciences 2008 (2008): 1–31. http://dx.doi.org/10.1155/2008/291968.

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Motivated by seismological problems, we have studied a fourth-order split scheme for the elastic wave equation. We split in the spatial directions and obtain locally one-dimensional systems to be solved. We have analyzed the new scheme and obtained results showing consistency and stability. We have used the split scheme to solve problems in two and three dimensions. We have also looked at the influence of singular forcing terms on the convergence properties of the scheme.

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41

Kristiansen, U. R., A. Krokstad, and T. Follestad. "Extending the image method to higher-order reflections." Applied Acoustics 38, no. 2-4 (1993): 195–206. http://dx.doi.org/10.1016/0003-682x(93)90051-7.

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42

Varonos, Agamemnon A., and George C. Bergeles. "A multigrid method with higher-order discretization schemes." International Journal for Numerical Methods in Fluids 35, no. 4 (2001): 395–420. http://dx.doi.org/10.1002/1097-0363(20010228)35:4<395::aid-fld97>3.0.co;2-v.

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43

Tongue, B. H., and K. Gu. "A higher order method of interpolated cell mapping." Journal of Sound and Vibration 125, no. 1 (August 1988): 169–79. http://dx.doi.org/10.1016/0022-460x(88)90424-5.

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44

Wang, Zhu, Ji Chen, and Yinchao Chen. "Development of a higher-order ADI-FDTD method." Microwave and Optical Technology Letters 37, no. 1 (February 24, 2003): 8–12. http://dx.doi.org/10.1002/mop.10808.

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45

Deep, Gagan, and Ioannis K. Argyros. "Improved Higher Order Compositions for Nonlinear Equations." Foundations 3, no. 1 (January 6, 2023): 25–36. http://dx.doi.org/10.3390/foundations3010003.

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In the present study, two new compositions of convergence order six are presented for solving nonlinear equations. The first method is obtained from the third-order one given by Homeier using linear interpolation, and the second one is obtained from the third-order method given by Traub using divided differences. The first method requires three evaluations of the function and one evaluation of the first derivative, thereby enhancing the efficiency index. In the second method, the computation of a derivative is reduced by approximating it using divided differences. Various numerical experiments are performed which demonstrate the accuracy and efficacy of the proposed methods.

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46

Jnawali, Jivandhar. "Higher Order Convergent Newton Type Iterative Methods." Journal of Nepal Mathematical Society 1, no. 2 (August 5, 2018): 32–39. http://dx.doi.org/10.3126/jnms.v1i2.41488.

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Newton method is one of the most widely used numerical methods for solving nonlinear equations. McDougall and Wotherspoon [Appl. Math. Lett., 29 (2014), 20-25] modified this method in predictor-corrector form and get an order of convergence 1+√2. More on the PDF

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47

Chen, D. J. L., J. C. Chang, and C. H. Cheng. "Higher order composition Runge-Kutta methods." Tamkang Journal of Mathematics 39, no. 3 (September 30, 2008): 199–211. http://dx.doi.org/10.5556/j.tkjm.39.2008.12.

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We derive a ﬁfth order ﬁve-stage explicit Runge-Kutta composition method, and an error estimator using linear combination of stage values and output values over two steps. Numerical results presented by testing the new pair over DETEST problems show a signiﬁcant improvement.

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48

Hutton, Graham. "Higher-order functions for parsing." Journal of Functional Programming 2, no. 3 (July 1992): 323–43. http://dx.doi.org/10.1017/s0956796800000411.

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AbstractIn combinator parsing, the text of parsers resembles BNF notation. We present the basic method, and a number of extensions. We address the special problems presented by white-space, and parsers with separate lexical and syntactic phases. In particular, a combining form for handling the ‘offside rule’ is given. Other extensions to the basic method include an ‘into’ combining form with many useful applications, and a simple means by which combinator parsers can produce more informative error messages.

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49

Fabiano, Nicola, and Nikola Mirkov. "Saddle point approximation to Higher order." Vojnotehnicki glasnik 70, no. 2 (2022): 447–60. http://dx.doi.org/10.5937/vojtehg70-33507.

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Introduction/purpose: Saddle point approximation has been considered in the paper Methods: The saddle point method is used in several different fields of mathematics and physics. Several terms of the expansion for the factorial function have been explicitely computed. Results: The integrals estimated in this way have values close to the exact one. Conclusions: Higher order corrections are not negligible even when requiring moderate levels of precision.

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50

Katsura, Hiroyuki, Naoki Kobayashi, and Ryosuke Sato. "Higher-Order Property-Directed Reachability." Proceedings of the ACM on Programming Languages 7, ICFP (August 30, 2023): 48–77. http://dx.doi.org/10.1145/3607831.

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The property-directed reachability (PDR) has been used as a successful method for automated verification of first-order transition systems. We propose a higher-order extension of PDR, called HoPDR, where higher-order recursive functions may be used to describe transition systems. We formalize HoPDR for the validity checking problem for conjunctive nu-HFL(Z), a higher-order fixpoint logic with integers and greatest fixpoint operators. The validity checking problem can also be viewed as a higher-order extension of the satisfiability problem for Constrained Horn Clauses (CHC), and safety property verification of higher-order programs can naturally be reduced to the validity checking problem. We have implemented a prototype verification tool based on HoPDR and confirmed its effectiveness. We also compare our HoPDR procedure with the PDR procedure for first-order systems and previous methods for fully automated higher-order program verification.

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