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Journal articles on the topic 'Finites differences'

Author: Grafiati

Published: 23 November 2024

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1

Mendonça, Agostinho, and M. Lurdes Lopes. "Pre-Tensioned Geogrids Reinforced Soil Structures with Face Panels in Fiber Glass." Materials Science Forum 587-588 (June 2008): 857–61. http://dx.doi.org/10.4028/www.scientific.net/msf.587-588.857.

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This paper presents an innovative technology for soil reinforced structures. The technology is based on the use of pre-tensioned geogrids reinforcements and face panels reinforced with fiber glass. Main technology advantages are: i) the very light face with great variety of geometries, size, color and surface textures; ii) either the face and the reinforcements are corrosion free; iii) the good behavior under seismic actions; iv) reduction of structure horizontal strains due to the pre-tension. First, the state of art on reinforced soil structures is done and then the constituents of the new technology are presented followed by the reference to the main theoretical principles considered in its conception. Secondly, numerical data from the behavior, in static conditions, of geogrid reinforced soil structures with and without pre-tensioned reinforcements are presented. In the numerical study the FLAC program, based on the differences finites method, will be used. The construction of the structures will be modeled considering the sequential placement of soil layers and reinforcements, enhancing the deformation behavior of the structures. Thirdly, the advantages of the new technology against the traditional ones are quantified, based on the results of the numerical studies. Special relevance will be given to face horizontal deformations and reinforcements strains. Finally, the main conclusions about the new technology will be put forward and its main advantages towards traditional technologies will be listed. Application fields where the technology is competitiveness will be identified.

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2

Lugo Jiménez, Abdul Abner, Guelvis Enrique Mata Díaz, and Bladismir Ruiz. "A comparative analysis of methods: mimetics, finite differences and finite elements for 1-dimensional stationary problems." Selecciones Matemáticas 8, no. 1 (June 30, 2021): 1–11. http://dx.doi.org/10.17268/sel.mat.2021.01.01.

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Numerical methods are useful for solving differential equations that model physical problems, for example, heat transfer, fluid dynamics, wave propagation, among others; especially when these cannot be solved by means of exact analysis techniques, since such problems present complex geometries, boundary or initial conditions, or involve non-linear differential equations. Currently, the number of problems that are modeled with partial differential equations are diverse and these must be addressed numerically, so that the results obtained are more in line with reality. In this work, a comparison of the classical numerical methods such as: the finite difference method (FDM) and the finite element method (FEM), with a modern technique of discretization called the mimetic method (MIM), or mimetic finite difference method or compatible method, is approached. With this comparison we try to conclude about the efficiency, order of convergence of these methods. Our analysis is based on a model problem with a one-dimensional boundary value, that is, we will study convection-diffusion equations in a stationary regime, with different variations in the gradient, diffusive coefficient and convective velocity.

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3

Jones, Michael A. "A Difference Equation Approach to Finite Differences of Polynomials." College Mathematics Journal 51, no. 5 (November 12, 2020): 375–77. http://dx.doi.org/10.1080/07468342.2020.1760065.

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4

Kazhikenova, S. Sh. "FINITE DIFFERENCE METHOD IMPLEMENTATION FOR NUMERICALINTEGRATION HYDRODYNAMIC EQUATIONS MELTS." Eurasian Physical Technical Journal 17, no. 1 (June 2020): 145–50. http://dx.doi.org/10.31489/2020no1/145-150.

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5

Carpenter, Mark H., and John Otto. "High-Order "Cyclo-Difference" Techniques: An Alternative to Finite Differences." Journal of Computational Physics 118, no. 2 (May 1995): 242–60. http://dx.doi.org/10.1006/jcph.1995.1096.

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6

S, Aiswarya, and Gerly T G. "Finite Series Solution Arising from Three-Dimensional q-Difference Equation." Journal of Computational Mathematica 2, no. 2 (December 30, 2018): 41–50. http://dx.doi.org/10.26524/cm38.

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7

Ochilov, Sherali Baratovich, Gulrukh Djumanazarovna Khasanova, and Oisha Kurbanovna Khudayberdieva. "Method For Constructing Correlation Dependences For Functions Of Many Variables Used Finite Differences." American Journal of Management and Economics Innovations 03, no. 05 (May 31, 2021): 46–52. http://dx.doi.org/10.37547/tajmei/volume03issue05-08.

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The article considers a method for constructing correlation models for finite-type functions using a set of variables. The use of the method of unknown squares in the construction of correlation models and the construction of higher-quality models is also justified. The proposed correlation models are considered on the example of statistical data of the Bukhara region of the Republic of Uzbekistan.

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8

Kratz, Werner. "An inequality for finite differences via asymptotics of Riccati matrix difference equations." Journal of Difference Equations and Applications 4, no. 3 (January 1998): 229–46. http://dx.doi.org/10.1080/10236199808808140.

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9

Kawada, Naoki, Takeshi Yoda, Norio Tagawa, Takao Tsuchiya, and Kan Okubo. "Evaluation of Acoustic Simulation Using Wave Equation Finite Difference Time Domain Method with Compact Finite Differences." Japanese Journal of Applied Physics 51, no. 7S (July 1, 2012): 07GG06. http://dx.doi.org/10.7567/jjap.51.07gg06.

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10

Kawada, Naoki, Takeshi Yoda, Norio Tagawa, Takao Tsuchiya, and Kan Okubo. "Evaluation of Acoustic Simulation Using Wave Equation Finite Difference Time Domain Method with Compact Finite Differences." Japanese Journal of Applied Physics 51 (July 20, 2012): 07GG06. http://dx.doi.org/10.1143/jjap.51.07gg06.

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11

Adam, David. "Finite differences in finite characteristic." Journal of Algebra 296, no. 1 (February 2006): 285–300. http://dx.doi.org/10.1016/j.jalgebra.2005.05.036.

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12

T G, Gerly, Dominic Babu G, and Mohan B. "Sum of Finite and Infinite Series Derived by Generalized Mixed Difference Equation." Journal of Computational Mathematica 1, no. 2 (December 30, 2017): 18–28. http://dx.doi.org/10.26524/cm12.

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13

Nóbrega, Jaldair, André Luis Santos Hortelan, Carlos Henrique Portezani, and Eriton Botero. "A study of nanomaterial transportation in the soil by finite difference approximations." Research in Agricultural Engineering 66, No. 4 (December 30, 2020): 146–55. http://dx.doi.org/10.17221/71/2019-rae.

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Although there has been an increase in the production and use of nanomaterials; few studies have analysed their contact with the environment and the consequent effects on an ecosystem's health, ranging from the impact on the growth of organisms to the contamination of water reservoirs. This work proposes a tool to study the transportation of nanomaterials in the soil by the finite difference method, modelling the dispersion of nanomaterials into the soil layers to estimate the environmental impact. The model validation was conducted through numerical simulations of manganese and zinc in contact with a compacted latosol. The results show that the nanoparticle pollutants move slowly through the layers and the highest concentration is found close to the source. Also, the Mn nanoparticles are in higher concentration than Zinc nanoparticles as a function of depth in the soil layers. The method generates more accurate simulated results in less time and provides a low-cost prediction of the environmental impact. Furthermore, the estimated environmental impacts can be used as a first approximation for the mitigation of the degraded area.

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14

Zhang Yabin, 张雅彬, 陈贤瑞 Chen Xianrui, 刘磊 Liu Lei, 刘彬 Liu Bin, 钟志 Zhong Zhi, and 单明广 Shan Mingguang. "基于快速迭代有限差分强度传输方程的相位恢复." Acta Optica Sinica 41, no. 22 (2021): 2212004. http://dx.doi.org/10.3788/aos202141.2212004.

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15

M.S. Nyachwaya, Nelson, Johana K. Sigey, Jeconiah A. Okelo, and James M. Okwoyo. "Finite Difference Solution of Seepage Equation: A Mathematical Model for Fluid Flow." SIJ Transactions on Computer Science Engineering & its Applications (CSEA) 02, no. 03 (June 6, 2014): 16–24. http://dx.doi.org/10.9756/sijcsea/v2i3/0204290101.

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16

WU, Long, Michihisa TSUTAHARA, and Shinsuke TAJIRI. "631 Finite difference lattice Boltzmann method for incompressible flow using acceleration modification." Proceedings of The Computational Mechanics Conference 2006.19 (2006): 531–32. http://dx.doi.org/10.1299/jsmecmd.2006.19.531.

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17

Omkar, R., M. Lalu, and K. Phaneendra. "Numerical solution of differential-difference equations having an interior layer using nonstandard finite differences." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 110, no. 2 (June 30, 2023): 104–15. http://dx.doi.org/10.31489/2023m2/104-115.

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This paper addresses the solution of a differential-difference type equation having an interior layer behaviour. A difference scheme is suggested to solve this equation using a non-standard finite difference method. Finite differences are derived from the first and second order derivatives. Using these approximations, the given equation is discretized. The discretized equation is solved using the algorithm for the tridiagonal system. The method is examined for convergence. Numerical examples are illustrated to validate the method. Maximum errors in the solution, in contrast to the other methods are organized to justify the method. The layer behaviour in the solution of the examples is depicted in graphs.

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18

Kumar, Anand. "Isotropic finite-differences." Journal of Computational Physics 201, no. 1 (November 2004): 109–18. http://dx.doi.org/10.1016/j.jcp.2004.05.005.

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19

Dinh, Ta Van. "On multi-parameter error expansions in finite difference methods for linear Dirichlet problems." Applications of Mathematics 32, no. 1 (1987): 16–24. http://dx.doi.org/10.21136/am.1987.104232.

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20

Ghuge, Vijaymala, T. L. Holambe, Bhausaheb Sontakke, and Gajanan Shrimangale. "Solving Time-fractional Order Radon Diffusion Equation in Water by Finite Difference Method." Indian Journal Of Science And Technology 17, no. 19 (May 14, 2024): 1994–2001. http://dx.doi.org/10.17485/ijst/v17i19.868.

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Objective: The aim of this research is to gain a comprehensive understanding of radon diffusion equation in water. Methods: A time fractional radon diffusion equation with Caputo sense is employed to find diffusion dynamics of radon in water medium. The fractional order explicit finite difference technique is used to find its numerical solution. A Python software is used to find numerical solution. Findings: The effect of fractional-order parameters on the distribution and concentration profiles of radon in water has been investigated. Furthermore, we study stability and convergence of the explicit finite difference method. Novelty: The fractional order explicit finite difference method can be used to estimate approximate solution of such fractional order differential equations. Keywords: Radon Diffusion Equation, Finite Difference Method, Caputo, Fractional Derivative, Python

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21

Thomée, Vidar. "From finite differences to finite elements." Journal of Computational and Applied Mathematics 128, no. 1-2 (March 2001): 1–54. http://dx.doi.org/10.1016/s0377-0427(00)00507-0.

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22

Triana, Juan, and Luis Ferro. "Finite difference methods in image processing." Selecciones Matemáticas 8, no. 02 (November 30, 2021): 411–16. http://dx.doi.org/10.17268/sel.mat.2021.02.17.

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23

Sirkes, Ziv, and Eli Tziperman. "Finite Difference of Adjoint or Adjoint of Finite Difference?" Monthly Weather Review 125, no. 12 (December 1997): 3373–78. http://dx.doi.org/10.1175/1520-0493(1997)125<3373:fdoaoa>2.0.co;2.

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24

Krylov, N. V. "Interior estimates for second-order differences of solutions of finite-difference elliptic Bellman’s equations." Mathematics of Computation 82, no. 283 (March 5, 2013): 1463–87. http://dx.doi.org/10.1090/s0025-5718-2013-02684-1.

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25

Saeed, Rostam K., and Mohammed I. Sadeeq. "Numerical Solution of Nonlinear Whitham-Broer-Kaup Shallow Water Model Using Finite Difference Methods." Journal of Zankoy Sulaimani - Part A 19, no. 1 (October 16, 2016): 197–210. http://dx.doi.org/10.17656/jzs.10597.

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26

Abdigaliyeva, А. N. "Modelling of the turbulent energy decay based on the finite-difference and spectral methods." International Journal of Mathematics and Physics 7, no. 1 (2016): 4–9. http://dx.doi.org/10.26577/2218-7987-2016-7-1-4-9.

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27

Fornberg, Bengt. "Finite difference method." Scholarpedia 6, no. 10 (2011): 9685. http://dx.doi.org/10.4249/scholarpedia.9685.

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28

Roeger, Lih-Ing Wu, and Ronald E. Mickens. "Exact finite difference and non-standard finite difference schemes for." Journal of Difference Equations and Applications 18, no. 9 (September 2012): 1511–17. http://dx.doi.org/10.1080/10236198.2011.574622.

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29

Kobus, Jacek. "Finite-difference versus finite-element methods." Chemical Physics Letters 202, no. 1-2 (1993): 7–12. http://dx.doi.org/10.1016/0009-2614(93)85342-l.

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30

Krylov, N. V. "Interior Estimates for the First-Order Differences for Finite-Difference Approximations for Elliptic Bellman’s Equations." Applied Mathematics & Optimization 65, no. 3 (January 4, 2012): 349–70. http://dx.doi.org/10.1007/s00245-011-9159-4.

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31

Wehrse, R. "Radiative Transfer with Finite Differences and Finite Elements." EAS Publications Series 28 (2008): 129–34. http://dx.doi.org/10.1051/eas:0828018.

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32

Rajeshwari, S., and B. Sheebakousar. "Единственность целых функциях относительно их разностных операторов и производных." Владикавказский математический журнал, no. 1 (March 23, 2023): 81–92. http://dx.doi.org/10.46698/p5608-0614-8805-b.

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In this paper we study the uniqueness of entire functions concerning their difference operator and derivatives. The idea of entire and meromorphic functions relies heavily on this direction. Rubel and Yang considered the uniqueness of entire function and its derivative and proved that if $f(z)$ and $f'(z)$ share two values $a,b$ counting multilicities then $f(z)\equiv f'(z)$. Later, Li Ping and Yang improved the result given by Rubel and Yang and proved that if $f(z)$ is a non-constant entire function and $a,b$ are two finite distinct complex values and if $f(z)$ and $f^{(k)}(z)$ share $a$ counting multiplicities and $b$ ignoring multiplicities then $f(z)\equiv f^{(k)}(z)$. In recent years, the value distribution of meromorphic functions of finite order with respect to difference analogue has become a subject of interest. By replacing finite distinct complex values by polynomials, we prove the following result: Let $\Delta f(z)$ be trancendental entire functions of finite order, $ k \geq 0$ be integer and $P_{1}$ and $P_{2}$ be two polynomials. If $\Delta f(z)$ and $f^{(k)}$ share $P_{1}$ CM and share $P_{2}$ IM, then $\Delta f \equiv f^{(k)}$. A non-trivial proof of this result uses Nevanlinna's value distribution theory.

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33

Stern, M. D., and Gordon Reece. "Microcomputer Modelling by Finite Differences." Mathematical Gazette 71, no. 458 (December 1987): 332. http://dx.doi.org/10.2307/3617088.

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34

Rhoads, Kathryn, and James A. Mendoza Alvarez. "Data Modeling Using Finite Differences." Mathematics Teacher 110, no. 9 (May 2017): 709–13. http://dx.doi.org/10.5951/mathteacher.110.9.0709.

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The Common Core State Standards for Mathematics (CCSSM) states that high school students should be able to recognize patterns of growth in linear, quadratic, and exponential functions and construct such functions from tables of data (CCSSI 2010). Accordingly, many high school curricula include a method that uses finite differences between data points to generate polynomial functions. That is, students may examine differences between successive output values (called first differences), successive differences of the first differences (second differences), or successive differences of the (n - 1)th differences (nth-order differences), and rely on the following:

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35

Chen, E. Jack. "Derivative Estimation with Finite Differences." SIMULATION 79, no. 10 (October 2003): 598–609. http://dx.doi.org/10.1177/0037549703039951.

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36

Wenchang, Chu. "Finite differences and determinant identities." Linear Algebra and its Applications 430, no. 1 (January 2009): 215–28. http://dx.doi.org/10.1016/j.laa.2007.08.044.

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37

Magnier, Sophie‐Adélade, Peter Mora, and Albert Tarantola. "Finite differences on minimal grids." GEOPHYSICS 59, no. 9 (September 1994): 1435–43. http://dx.doi.org/10.1190/1.1443700.

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Conventional approximations to space derivatives by finite differences use orthogonal grids. To compute second‐order space derivatives in a given direction, two points are used. Thus, 2N points are required in a space of dimension N; however, a centered finite‐difference approximation to a second‐order derivative may be obtained using only three points in 2-D (the vertices of a triangle), four points in 3-D (the vertices of a tetrahedron), and in general, N + 1 points in a space of dimension N. A grid using N + 1 points to compute derivatives is called minimal. The use of minimal grids does not introduce any complication in programming and suppresses some artifacts of the nonminimal grids. For instance, the well‐known decoupling between different subgrids for isotropic elastic media does not happen when using minimal grids because all the components of a given tensor (e.g., displacement or stress) are known at the same points. Some numerical tests in 2-D show that the propagation of waves is as accurate as when performed with conventional grids. Although this method may have less intrinsic anisotropies than the conventional method, no attempt has yet been made to obtain a quantitative estimation.

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38

Spivey, Michael Z. "Combinatorial sums and finite differences." Discrete Mathematics 307, no. 24 (November 2007): 3130–46. http://dx.doi.org/10.1016/j.disc.2007.03.052.

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39

Brighi, Bernard, Michel Chipot, and Erich Gut. "Finite differences on triangular grids." Numerical Methods for Partial Differential Equations 14, no. 5 (September 1998): 567–79. http://dx.doi.org/10.1002/(sici)1098-2426(199809)14:5<567::aid-num2>3.0.co;2-g.

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40

Jerome, John Soundar. "Identities arising from finite differences." Resonance 9, no. 11 (November 2004): 68–71. http://dx.doi.org/10.1007/bf02834974.

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41

Iserles, A. "Order Stars, Approximations and Finite Differences. III Finite Differences for $u_t = \omega u_{xx} $." SIAM Journal on Mathematical Analysis 16, no. 5 (September 1985): 1020–33. http://dx.doi.org/10.1137/0516076.

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42

Кривовичев, Г. В., and С. А. Михеев. "Stability study of finite-difference-based lattice Boltzmann schemes with upwind differences of high order approximation." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 2 (June 30, 2015): 196–204. http://dx.doi.org/10.26089/nummet.v16r220.

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Исследуется устойчивость трехслойных конечно-разностных решеточных схем Больцмана третьего и четвертого порядков аппроксимации по пространственным переменным. Проводится анализ устойчивости по начальным условиям с использованием линейного приближения. Для исследования используется метод Неймана. Показано, что устойчивость схем можно улучшить за счет аппроксимации конвективных членов во внутренних узлах сеточного шаблона. В этом случае удается получать большие по площади области устойчивости, чем при аппроксимации в граничных узлах шаблона. The stability of three-level finite-difference-based lattice Boltzmann schemes of third and fourth orders of approximation with respect to spatial variables is studied. The stability analysis with respect to initial conditions is performed on the basis of a linear approximation. These studies are based on the Neumann method. It is shown that the stability of the schemes can be improved by the approximation convective terms in internal nodes of the grid stencils in use. In this case the stability domains are larger compared to the case of approximation in boundary nodes.

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43

Vanderveken, Frederic, Jeroen Mulkers, Jonathan Leliaert, Bartel Van Waeyenberge, Bart Sorée, Odysseas Zografos, Florin Ciubotaru, and Christoph Adelmann. "Finite difference magnetoelastic simulator." Open Research Europe 1 (April 19, 2021): 35. http://dx.doi.org/10.12688/openreseurope.13302.1.

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We describe an extension of the micromagnetic finite difference simulation software MuMax3 to solve elasto-magneto-dynamical problems. The new module allows for numerical simulations of magnetization and displacement dynamics in magnetostrictive materials and structures, including both direct and inverse magnetostriction. The theoretical background is introduced, and the implementation of the extension is discussed. The magnetoelastic extension of MuMax3 is freely available under the GNU General Public License v3.

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44

Mickens, Ronald E. "Nonstandard Finite Difference Schemes." Notices of the American Mathematical Society 65, no. 01 (January 1, 2018): 17–18. http://dx.doi.org/10.1090/noti1617.

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45

Fishburn, Peter C., Helen M. Marcus-Roberts, and Fred S. Roberts. "Unique Finite Difference Measurement." SIAM Journal on Discrete Mathematics 1, no. 3 (August 1988): 334–54. http://dx.doi.org/10.1137/0401034.

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46

Wade, Bruce A. "Symmetrizable finite difference operators." Mathematics of Computation 54, no. 190 (May 1, 1990): 525. http://dx.doi.org/10.1090/s0025-5718-1990-1011447-9.

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47

Cao, S., and K. J. Muirhead. "Finite difference modelling ofLgblockage." Geophysical Journal International 115, no. 1 (October 1993): 85–96. http://dx.doi.org/10.1111/j.1365-246x.1993.tb05590.x.

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48

Killingbeck, J. "Accurate finite difference eigenvalues." Physics Letters A 115, no. 7 (April 1986): 301–3. http://dx.doi.org/10.1016/0375-9601(86)90615-8.

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49

Riza, Mustafa, Ali Özyapici, and Emine Misirli. "Multiplicative finite difference methods." Quarterly of Applied Mathematics 67, no. 4 (May 14, 2009): 745–54. http://dx.doi.org/10.1090/s0033-569x-09-01158-2.

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50

Ristow, Dietrich, and Thomas Rühl. "Fourier finite‐difference migration." GEOPHYSICS 59, no. 12 (December 1994): 1882–93. http://dx.doi.org/10.1190/1.1443575.

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Many existing migration schemes cannot simultaneously handle the two most important problems of migration: imaging of steep dips and imaging in media with arbitrary velocity variations in all directions. For example, phase‐shift (ω, k) migration is accurate for nearly all dips but it is limited to very simple velocity functions. On the other hand, finite‐difference schemes based on one‐way wave equations consider arbitrary velocity functions but they attenuate steeply dipping events. We propose a new hybrid migration method, named “Fourier finite‐difference migration,” wherein the downward‐continuation operator is split into two downward‐continuation operators: one operator is a phase‐shift operator for a chosen constant background velocity, and the other operator is an optimized finite‐difference operator for the varying component of the velocity function. If there is no variation of velocity, then only a phase‐shift operator will be applied automatically. On the other hand, if there is a strong variation of velocity, then the phase‐shift component is suppressed and the optimized finite‐difference operator will be fully applied. The cascaded application of phase‐shift and finite‐difference operators shows a better maximum dip‐angle behavior than the split‐step Fourier migration operator. Depending on the macro velocity model, the Fourier finite‐difference migration even shows an improved performance compared to conventional finite‐difference migration with one downward‐continuation step. Finite‐difference migration with two downward‐continuation steps is required to reach the same migration performance, but this is achieved with about 20 percent higher computation costs. The new cascaded operator of the Fourier finite‐difference migration can be applied to arbitrary velocity functions and allows an accurate migration of steeply dipping reflectors in a complex macro velocity model. The dip limitation of the cascaded operator depends on the variation of the velocity field and, hence, is velocity‐adaptive.

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