Journal articles: 'Finite differences'

1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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:

9

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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10

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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11

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.

12

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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13

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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14

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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15

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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16

O'Leary, D. P. "Finite Differences and Finite Elements: Getting to Know You." Computing in Science and Engineering 7, no. 3 (May 2005): 72–79. http://dx.doi.org/10.1109/mcse.2005.49.

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17

Yano, H., A. Kieda, and K. Nishioka. "A combined scheme of finite elements and finite differences." Journal of the Franklin Institute 326, no. 1 (January 1989): 131–37. http://dx.doi.org/10.1016/0016-0032(89)90065-3.

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18

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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19

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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20

Selmin, V. "The node-centred finite volume approach: Bridge between finite differences and finite elements." Computer Methods in Applied Mechanics and Engineering 102, no. 1 (January 1993): 107–38. http://dx.doi.org/10.1016/0045-7825(93)90143-l.

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21

Bossavit, A. "'Generalized Finite Differences' in Computational Electromagnetics." Progress In Electromagnetics Research 32 (2001): 45–64. http://dx.doi.org/10.2528/pier00080102.

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22

Chu, W. "Finite Differences and Terminating Hypergeometric Series." Irish Mathematical Society Bulletin 0078 (2016): 31–45. http://dx.doi.org/10.33232/bims.0078.31.45.

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23

Levant, Arie. "Finite Differences in Homogeneous Discontinuous Control." IEEE Transactions on Automatic Control 52, no. 7 (July 2007): 1208–17. http://dx.doi.org/10.1109/tac.2007.900825.

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24

Seaton, K. A., and J. Armstrong. "Polynomial cancellation coding and finite differences." IEEE Transactions on Information Theory 46, no. 1 (2000): 311–13. http://dx.doi.org/10.1109/18.817533.

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25

Gyarmati, Katalin, François Hennecart, and Imre Z. Ruzsa. "Sums and differences of finite sets." Functiones et Approximatio Commentarii Mathematici 37, no. 1 (January 2007): 175–86. http://dx.doi.org/10.7169/facm/1229618749.

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26

Monserrat, Bartomeu. "Electron–phonon coupling from finite differences." Journal of Physics: Condensed Matter 30, no. 8 (February 1, 2018): 083001. http://dx.doi.org/10.1088/1361-648x/aaa737.

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27

Brezzi, Franco, Annalisa Buffa, and Konstantin Lipnikov. "Mimetic finite differences for elliptic problems." ESAIM: Mathematical Modelling and Numerical Analysis 43, no. 2 (December 5, 2008): 277–95. http://dx.doi.org/10.1051/m2an:2008046.

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28

Marcone, Alberto, Franco Parlamento, and Alberto Policriti. "Finite families with few symmetric differences." Proceedings of the American Mathematical Society 127, no. 3 (1999): 835–45. http://dx.doi.org/10.1090/s0002-9939-99-04751-6.

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29

Adam, David, and Youssef Fares. "Integer-valued Euler–Jackson’s finite differences." Monatshefte für Mathematik 161, no. 1 (April 2, 2009): 15–32. http://dx.doi.org/10.1007/s00605-009-0111-5.

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30

Ballantine, Cristina, and Mircea Merca. "Finite differences of Euler's zeta function." Miskolc Mathematical Notes 18, no. 2 (2017): 639. http://dx.doi.org/10.18514/mmn.2017.2256.

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31

Allen, Paul T. "Boundary Value Problems and Finite Differences." College Mathematics Journal 47, no. 1 (January 2016): 34–41. http://dx.doi.org/10.4169/college.math.j.47.1.34.

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32

Leitão, V. M. A. "Generalized finite differences using fundamental solutions." International Journal for Numerical Methods in Engineering 81, no. 5 (July 24, 2009): 564–83. http://dx.doi.org/10.1002/nme.2697.

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33

Li, Brandon. "2D Microwave Simulation Using Finite Differences." Cornell Undergraduate Research Journal 1, no. 1 (April 28, 2022): 74–83. http://dx.doi.org/10.37513/curj.v1i1.659.

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We derive a finite difference scheme to numerically simulate the propagation of microwaves in a 2D domain with reflective obstacles. An analysis of the consistency and stability of this method is performed, leading to a rigorous justification of its convergence. Following this, we discuss the boundary conditions and derive the mathematical form for energy flux. Finally, the numerical approximation is compared against prior experimental results. The simulation was found to have been able to predict the distribution of interference maxima and minima with some accuracy, but it was seen to be less effective in predicting average intensities. The advantages and disadvantages of these techniques are then discussed along with possible avenues for improvement.

34

Song, Xiaolei, Sergey Fomel, and Lexing Ying. "Lowrank finite-differences and lowrank Fourier finite-differences for seismic wave extrapolation in the acoustic approximation." Geophysical Journal International 193, no. 2 (February 28, 2013): 960–69. http://dx.doi.org/10.1093/gji/ggt017.

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35

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.

36

Boyd, John P. "Sum-accelerated pseudospectral methods: Finite differences and sech-weighted differences." Computer Methods in Applied Mechanics and Engineering 116, no. 1-4 (January 1994): 1–11. http://dx.doi.org/10.1016/s0045-7825(94)80003-0.

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37

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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38

Loula, Abimael F. D., Daniel T. Fernandes, and Rubem A. Silva. "Generalized finite element and finite differences methods for the Helmholtz problem." IOP Conference Series: Materials Science and Engineering 10 (June 1, 2010): 012157. http://dx.doi.org/10.1088/1757-899x/10/1/012157.

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39

Zegeling, Paul A. "r-refinement for evolutionary PDEs with finite elements or finite differences." Applied Numerical Mathematics 26, no. 1-2 (January 1998): 97–104. http://dx.doi.org/10.1016/s0168-9274(97)00086-x.

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40

Neta, Beny, and Jerome O. Igwe. "Finite differences versus finite elements for solving nonlinear integro-differential equations." Journal of Mathematical Analysis and Applications 112, no. 2 (December 1985): 607–18. http://dx.doi.org/10.1016/0022-247x(85)90266-5.

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41

Flores, B. E., J. P. Hennart, and E. del Valle. "Mesh-centered finite differences from unconventional mixed-hybrid nodal finite elements." Numerical Methods for Partial Differential Equations 22, no. 6 (2006): 1348–60. http://dx.doi.org/10.1002/num.20157.

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42

Hennart, J. P., and E. del Valle. "Mesh-centered finite differences from nodal finite elements for elliptic problems." Numerical Methods for Partial Differential Equations 14, no. 4 (July 1998): 439–65. http://dx.doi.org/10.1002/(sici)1098-2426(199807)14:4<439::aid-num2>3.0.co;2-l.

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43

Shestakov, A. I. "Comparison of finite differences and finite elements on a parabolic problem." Journal of Computational Physics 79, no. 1 (November 1988): 231–43. http://dx.doi.org/10.1016/0021-9991(88)90014-9.

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44

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.

45

Stanisławski, Rafał, and Krzysztof J. Latawiec. "Normalized finite fractional differences: Computational and accuracy breakthroughs." International Journal of Applied Mathematics and Computer Science 22, no. 4 (December 28, 2012): 907–19. http://dx.doi.org/10.2478/v10006-012-0067-9.

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This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated with the introduction of a perfect finite fractional difference and, in particular, a powerful adaptive finite fractional difference, whose excellent performance is illustrated in simulation examples.

46

Sirotina, Natalia, Anna Kopoteva, and Andrey Zatonskiy. "FINITE DIFFERENCES METHOD FOR SOCIO-ECONOMIC MODELING." Applied Mathematics and Control Sciences, no. 1 (April 14, 2021): 174–89. http://dx.doi.org/10.15593/2499-9873/2021.1.10.

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In the issue we consider socio-economic processes modeling based on first and second order finite differences models. Since commonly used modeling methods have drawbacks and thus are not universal it was necessary to develop alternative methods which are better in some aspects. Specifically multiple linear regression models have limited prediction abilities, and differential regression coefficient evaluation method is quite complex and have some economically uninterpreted excess tunings. In our research we replaced first and second order derivatives in differential regression models with their finite differences equivalents and thus gained a multiple linear regression model modification which includes first and second order auto regression items. Estimation of their parameters can be done using a modification of least-squares method in which we demand that factor coefficients signs for models with and without auto regression items are the same. Due to additional items in the modified linear regression models their approximation capacity is greater than of a common model. However for application purposes model forecasting capacity is more important, i.e. the forecasting efficiency criterion is the most significant for a decision making. In order to estimate forecasting potential of modified multiple linear regression models we performed coefficient estimation of unmodified and modified equations for 59 various socio-economic data sets. We used shortened time series, so we could calculate model values and compare them to actual data. It was determined that modified multiple linear regression models allowed to make better predictions in 49 (76.3 %) cases. We can now assume that addition of auto regression items into multiple linear regression model can increase short-term forecasting efficiency.

47

ERZAN, Ayşe. "Finite q-differences and the Renormalization Group." Turkish Journal of Physics 21, no. 1 (January 1, 1997): 179. http://dx.doi.org/10.55730/1300-0101.2477.

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48

Guillotte, Henry P. "The Method of Finite Differences: Some Applications." Mathematics Teacher 79, no. 6 (September 1986): 466–70. http://dx.doi.org/10.5951/mt.79.6.0466.

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49

Mango. "ON FINITE DIFFERENCES ON A STRING PROBLEM." Journal of Mathematics and Statistics 10, no. 2 (February 1, 2014): 139–47. http://dx.doi.org/10.3844/jmssp.2014.139.147.

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50

Chu, Wenchang. "Finite differences and Dixon-like binomial sums." Integral Transforms and Special Functions 23, no. 4 (April 2012): 251–61. http://dx.doi.org/10.1080/10652469.2011.571646.

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Journal articles on the topic 'Finite differences'

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