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Journal articles on the topic 'The finite difference method'

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Published: 30 May 2022
Last updated: 31 May 2022

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1

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

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2

Lipnikov, Konstantin, Gianmarco Manzini, and Mikhail Shashkov. "Mimetic finite difference method." Journal of Computational Physics 257 (January 2014): 1163–227. http://dx.doi.org/10.1016/j.jcp.2013.07.031.

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3

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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4

Killingbeck, John, and Georges Jolicard. "The virial finite difference method." Physics Letters A 228, no. 4-5 (April 1997): 205–7. http://dx.doi.org/10.1016/s0375-9601(97)00092-3.

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5

Lopez-Mago, Dorilian, and Julio C. Gutiérrez-Vega. "Adaptive boundaryless finite-difference method." Journal of the Optical Society of America A 30, no. 2 (January 31, 2013): 259. http://dx.doi.org/10.1364/josaa.30.000259.

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6

Venkata Sai Jitin, Jami Naga, and Atul Ramesh Bhagat. "Inverse conduction method using finite difference method." IOP Conference Series: Materials Science and Engineering 377 (June 2018): 012015. http://dx.doi.org/10.1088/1757-899x/377/1/012015.

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7

E. Griffith, Boyce, and Xiaoyu Luo. "Hybrid finite difference/finite element immersed boundary method." International Journal for Numerical Methods in Biomedical Engineering 33, no. 12 (August 16, 2017): e2888. http://dx.doi.org/10.1002/cnm.2888.

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8

Banerjee, Arjun. "The Method of Finite Difference Regression." Open Journal of Statistics 08, no. 01 (2018): 49–68. http://dx.doi.org/10.4236/ojs.2018.81005.

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9

Ying, Lung-an, and Xin-ting Zhang. "Finite difference method for detonation waves." Journal of Computational and Applied Mathematics 159, no. 1 (October 2003): 185–93. http://dx.doi.org/10.1016/s0377-0427(03)00558-2.

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10

Takasawa, Yoshimitsu. "Numerical dispersion of finite difference method." Journal of the Acoustical Society of America 120, no. 5 (November 2006): 3364. http://dx.doi.org/10.1121/1.4781514.

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11

Doerr, Christopher R. "Sparse Finite Difference Time Domain Method." IEEE Photonics Technology Letters 25, no. 23 (December 2013): 2259–62. http://dx.doi.org/10.1109/lpt.2013.2285181.

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12

Abreu, R., D. Stich, and J. Morales. "The Complex-Step-Finite-Difference method." Geophysical Journal International 202, no. 1 (April 22, 2015): 72–93. http://dx.doi.org/10.1093/gji/ggv125.

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13

Mikhailov, M. D. "Finite difference method by using Mathematica." International Journal of Heat and Mass Transfer 37 (March 1994): 375–79. http://dx.doi.org/10.1016/0017-9310(94)90037-x.

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14

James, Matthew R. "An explicit finite difference method for finite-time observers." International Journal of Robust and Nonlinear Control 4, no. 6 (1994): 791–806. http://dx.doi.org/10.1002/rnc.4590040607.

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15

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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16

Jaśkowiec, J., and S. Milewski. "Coupling finite element method with meshless finite difference method in thermomechanical problems." Computers & Mathematics with Applications 72, no. 9 (November 2016): 2259–79. http://dx.doi.org/10.1016/j.camwa.2016.08.020.

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17

Yamauchi, Junji, Koji Nishio, and Hisamatsu Nakano. "Hybrid numerical technique combining the finite-difference beam-propagation method and the finite-difference time-domain method." Optics Letters 22, no. 5 (March 1, 1997): 259. http://dx.doi.org/10.1364/ol.22.000259.

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18

Tang, Hui, Xiao Jun Li, Guo Liang Zhou, and Chun Ming Zhang. "Finite/Explicit Finite Element - Finite Difference Coupling Method for Analysis of Soil - Foundation System." Advanced Materials Research 838-841 (November 2013): 913–17. http://dx.doi.org/10.4028/www.scientific.net/amr.838-841.913.

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There are some coupling methods based on Finite Element Method and some other numerical methods, such as Infinite Element Method, Boundary Element Method, Finite Difference Method, etc. But these methods have their own limitations on simulation the foundation. For overcome these disadvantages, a coupling method is presented in this paper, which be proposed to analyze the effect of soil - foundation on seismic response of structures. In this coupling method, the structure and the surrounding soil are simulated with Finite Element method, and the other part of the soil with Explicit Finite Element - Finite Difference Method. Compared to other coupling methods, it is more flexible and its calculation amount is acceptable. The accuracy and effectiveness of the coupling method have been verified through Numerical experiment in this paper.
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19

Robertsson, Johan O. A., Joakim O. Blanch, and William W. Symes. "Viscoelastic finite‐difference modeling." GEOPHYSICS 59, no. 9 (September 1994): 1444–56. http://dx.doi.org/10.1190/1.1443701.

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Real earth media disperse and attenuate propagating mechanical waves. This anelastic behavior can be described well by a viscoelastic model. We have developed a finite‐difference simulator to model wave propagation in viscoelastic media. The finite‐difference method was chosen in favor of other methods for several reasons. Finite‐difference codes are more portable than, for example, pseudospectral codes. Moreover, finite‐difference schemes provide a convenient environment in which to define complicated boundaries. A staggered scheme of second‐order accuracy in time and fourth‐order accuracy in space appears to be optimally efficient. Because of intrinsic dispersion, no fixed grid points per wavelength rule can be given; instead, we present tables, which enable a choice of grid parameters for a given level of accuracy. Since the scheme models energy absorption, natural and efficient absorbing boundaries may be implemented merely by changing the parameters near the grid boundary. The viscoelastic scheme is only marginally more expensive than analogous elastic schemes. The efficient implementation of absorbing boundaries may therefore be a good reason for also using the viscoelastic scheme in purely elastic simulations. We illustrate our method and the importance of accurately modeling anelastic media through 2-D and 3-D examples from shallow marine environments.
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20

FUKUNAGA, Yoshiko, Manabu ENOKI, and Teruo KISHI. "DYNAMIC GREEN'S FUNCTION OF FINITE MEDIA BY FINITE DIFFERENCE METHOD." Nondestructive Testing Communications 4, no. 2-3 (January 1988): 91. http://dx.doi.org/10.1080/02780898808962140.

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21

Fukunaga, Y., M. Enoki, T. Kishi, and J. Kihara. "Dynamic Green’s Function of Finite Media by Finite Difference Method." Journal of Vibration and Acoustics 112, no. 1 (January 1, 1990): 45–52. http://dx.doi.org/10.1115/1.2930097.

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A three-dimensional finite difference method (FDM) has been developed for the computation of elastic wave propagation in finite media containing a macrocrack, with a new treatment of boundary conditions of surfaces. The method can be used for the simulation of dynamic Green’s functions of an arbitrary rectangular parallelepiped medium with a macrocrack such as a compact tension (CT) specimen. The validity of the method has been confirmed by comparison with theoretical solutions of the plate problem for a monopole source and a double source. The method was then applied to the computation of Green’s functions for a seismic moment in CT specimen. Evaluation of Green’s function by this three-dimensional FDM leads to more accurate acoustic emission (AE) source characterization.
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22

ISHIKAWA, Mikihito, Toshihito OHMI, A. Toshimitsu YOKOBORI Jr., and Masaaki NISHIMURA. "OS1010 The Hydrogen Diffusion Analysis by Finite Element Method and Finite Difference Method." Proceedings of the Materials and Mechanics Conference 2014 (2014): _OS1010–1_—_OS1010–3_. http://dx.doi.org/10.1299/jsmemm.2014._os1010-1_.

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23

Huang, C., T. Long, and M. B. Liu. "Coupling finite difference method with finite particle method for modeling viscous incompressible flows." International Journal for Numerical Methods in Fluids 90, no. 11 (May 20, 2019): 564–83. http://dx.doi.org/10.1002/fld.4735.

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24

Liu, Renwei, Dongjie Wang, Xinyu Zhang, Wang Li, and Bo Yu. "Comparison Study on the Performances of Finite Volume Method and Finite Difference Method." Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/596218.

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Vorticity-stream function method and MAC algorithm are adopted to systemically compare the finite volume method (FVM) and finite difference method (FDM) in this paper. Two typical problems—lid-driven flow and natural convection flow in a square cavity—are taken as examples to compare and analyze the calculation performances of FVM and FDM with variant mesh densities, discrete forms, and treatments of boundary condition. It is indicated that FVM is superior to FDM from the perspective of accuracy, stability of convection term, robustness, and calculation efficiency. Particularly ,when the mesh is coarse and taken as20×20, the results of FDM suffer severe oscillation and even lose physical meaning.
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25

Gupta, Dr A. R. "Comparative analysis of Rectangular Plate by Finite element method and Finite Difference Method." International Journal for Research in Applied Science and Engineering Technology 9, no. 9 (September 30, 2021): 1399–402. http://dx.doi.org/10.22214/ijraset.2021.38153.

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Abstract: Analysis of rectangular plates is common when designing the foundation of civil, traffic, and irrigation works. The current research presents the results of the analysis of rectangular plates using the finite difference method and Finite Element Method. The results of the research verify the accuracy of the FEM and are in agreement with findings in the literature. The plate is analyzed considering it to be completely solid. The ordinary finite difference method is used to solve the governing differential equation of the plate deflection. The proposed method can be easily programmed to readily apply on a plate problem. The work covers the determination of displacement components at different points of the plate and checking the result by software (STAAD.Pro) analysis. Keywords: rectangular plate, FEM, Finite Difference Method
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26

Gupta, Dr A. R. "Comparative analysis of Rectangular Plate by Finite element method and Finite Difference Method." International Journal for Research in Applied Science and Engineering Technology 9, no. 9 (September 30, 2021): 1397–98. http://dx.doi.org/10.22214/ijraset.2021.38152.

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Abstract: Plates are commonly used to support lateral or vertical loads. Before the design of such a plate, analysis is performed to check the stability of plate for the proposed load. There are several methods for this analysis. In this research, a comparative analysis of rectangular plate is done between Finite Element Method (FEM) and Finite Difference Method (FDM). The plate is considered to be subjected to an arbitrary transverse uniformly distributed loading and is considered to be clamped at the two opposite edges and free at the other two edges. The Finite Element Method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for partial differential equations. It is also referred to as finite element analysis (FEA). FEM subdivides a large problem into smaller, simpler, parts, called finite elements. The work covers the determination of displacement components at different points of the plate and checking the result by software (STAAD.Pro) analysis. The ordinary Finite Difference Method (FDM) is used to solve the governing differential equation of the plate deflection. The proposed methods can be easily programmed to readily apply on a plate problem. Keywords: Arbitrary, FEM, FDM, boundary.
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27

Song, Xiaolei, and Sergey Fomel. "Fourier finite-difference wave propagation." GEOPHYSICS 76, no. 5 (September 2011): T123—T129. http://dx.doi.org/10.1190/geo2010-0287.1.

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We introduce a novel technique for seismic wave extrapolation in time. The technique involves cascading a Fourier transform operator and a finite-difference operator to form a chain operator: Fourier finite differences (FFD). We derive the FFD operator from a pseudoanalytical solution of the acoustic wave equation. Two-dimensional synthetic examples demonstrate that the FFD operator can have high accuracy and stability in complex-velocity media. Applying the FFD method to the anisotropic case overcomes some disadvantages of other methods, such as the coupling of qP-waves and qSV-waves. The FFD method can be applied to enhance accuracy and stability of seismic imaging by reverse time migration.
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28

Luo, Xiaolin, and Pavel V. Shevchenko. "Pricing TARNs Using a Finite Difference Method." Journal of Derivatives 23, no. 1 (August 31, 2015): 62–72. http://dx.doi.org/10.3905/jod.2015.23.1.062.

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29

Igboekwe, Magnus U., and N. J. Achi. "Finite Difference Method of Modelling Groundwater Flow." Journal of Water Resource and Protection 03, no. 03 (2011): 192–98. http://dx.doi.org/10.4236/jwarp.2011.33025.

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30

Anguelov, Roumen, and Jean M. S. Lubuma. "Nonstandard finite difference method by nonlocal approximation." Mathematics and Computers in Simulation 61, no. 3-6 (January 2003): 465–75. http://dx.doi.org/10.1016/s0378-4754(02)00106-4.

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31

Saitoh, I., Y. Suzuki, and N. Takahashi. "The symplectic finite difference time domain method." IEEE Transactions on Magnetics 37, no. 5 (2001): 3251–54. http://dx.doi.org/10.1109/20.952588.

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32

KOIBUCHI, Hiroshi. "Finite Difference Method on Triangulated Random Mesh." Transactions of the Japan Society of Mechanical Engineers Series B 57, no. 543 (1991): 3653–59. http://dx.doi.org/10.1299/kikaib.57.3653.

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33

NOR AZWADI, C. S., and T. TANAHASHI. "SIMPLIFIED FINITE DIFFERENCE THERMAL LATTICE BOLTZMANN METHOD." International Journal of Modern Physics B 22, no. 22 (September 10, 2008): 3865–76. http://dx.doi.org/10.1142/s0217979208048619.

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In this paper, a well-known finite difference technique is combined with thermal lattice Boltzmann method to solve 2-dimensional incompressible thermal fluid flow problems. A small number of microvelocity components are applied for the calculation of temperature field. The combination of finite difference with lattice Boltzmann method is found to be an efficient and stable approach for the simulation at high Rayleigh number of natural convection in a square cavity.
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34

Heinrich, W., K. Beilenhoff, P. Mezzanotte, and L. Roselli. "Optimum mesh grading for finite-difference method." IEEE Transactions on Microwave Theory and Techniques 44, no. 9 (1996): 1569–74. http://dx.doi.org/10.1109/22.536606.

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35

Sujecki, Slawomir. "Generalized rectangular finite difference beam propagation method." Applied Optics 47, no. 23 (August 8, 2008): 4280. http://dx.doi.org/10.1364/ao.47.004280.

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36

Chwang, Allen T., and Hamn‐Ching Chen. "Optimal Finite Difference Method for Potential Flows." Journal of Engineering Mechanics 113, no. 11 (November 1987): 1759–73. http://dx.doi.org/10.1061/(asce)0733-9399(1987)113:11(1759).

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37

Chang, Qian Shun, Bo Ling Guo, and Hong Jiang. "Finite difference method for generalized Zakharov equations." Mathematics of Computation 64, no. 210 (May 1, 1995): 537. http://dx.doi.org/10.1090/s0025-5718-1995-1284664-5.

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38

Pao-Lo Liu, Qida Zhao, and Fow-Sen Choa. "Slow-wave finite-difference beam propagation method." IEEE Photonics Technology Letters 7, no. 8 (August 1995): 890–92. http://dx.doi.org/10.1109/68.404005.

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39

Bychkov, E. V. "Finite Difference Method for Modified Boussinesq Equation." Journal of Computational and Engineering Mathematics 5, no. 4 (2018): 58–63. http://dx.doi.org/10.14529/jcem180405.

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40

Wang, Shumin, Robert Lee, and Fernando L. Teixeira. "Implicit nonstaggered finite-difference time-domain method." Microwave and Optical Technology Letters 45, no. 4 (2005): 317–19. http://dx.doi.org/10.1002/mop.20809.

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41

Opršal, Ivo, and Jiří Zahradník. "Elastic finite‐difference method for irregular grids." GEOPHYSICS 64, no. 1 (January 1999): 240–50. http://dx.doi.org/10.1190/1.1444520.

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Finite‐difference (FD) modeling of complicated structures requires simple algorithms. This paper presents a new elastic FD method for spatially irregular grids that is simple and, at the same time, saves considerable memory and computing time. Features like faults, low‐velocity layers, cavities, and/or nonplanar surfaces are treated on a fine grid, while the remaining parts of the model are, with equal accuracy, represented on a coarse grid. No interpolation is needed between the fine and coarse parts due to the rectangular grid cells. Relatively abrupt transitions between the small and large grid steps produce no numerical artifacts in the present method. Planar or nonplanar free surfaces, including underground cavities, are treated in a way similar to internal grid points but with consideration of the zero‐valued elastic parameters and density outside the free surface (vacuum formalism). A theoretical proof that vacuum formalism fullfills the free‐surface conditions is given. Numerical validation is performed through comparison with independent methods, comparing FD with explicitly prescribed boundary conditions and finite elements. Memory and computing time needed in the studied models was only about 10 to 40% of that employing regular square grids of equal accuracy. A practical example of a synthetic seismic section, showing clear signatures of a coal seam and cavity, is presented. The method can be extended to three dimensions.
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42

Chung, Y., N. Dagli, and L. Thylén. "Explicit finite difference vectorial beam propagation method." Electronics Letters 27, no. 23 (1991): 2119. http://dx.doi.org/10.1049/el:19911313.

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43

Ying, Lung-An. "Finite difference method for a combustion model." Mathematics of Computation 73, no. 246 (October 27, 2003): 595–612. http://dx.doi.org/10.1090/s0025-5718-03-01601-6.

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44

Abubakar, A., W. Hu, P. M. van den Berg, and T. M. Habashy. "A finite-difference contrast source inversion method." Inverse Problems 24, no. 6 (September 22, 2008): 065004. http://dx.doi.org/10.1088/0266-5611/24/6/065004.

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45

Schulz, D., C. Glingener, and E. Voges. "Novel generalized finite-difference beam propagation method." IEEE Journal of Quantum Electronics 30, no. 4 (April 1994): 1132–40. http://dx.doi.org/10.1109/3.291382.

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46

Masoudi, H. M., M. A. AlSunaidi, and J. M. Arnold. "Time-domain finite-difference beam propagation method." IEEE Photonics Technology Letters 11, no. 10 (October 1999): 1274–76. http://dx.doi.org/10.1109/68.789715.

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47

Li, Zi-Cai, Cheng-Sheng Chien, and Hung-Tsai Huang. "Effective condition number for finite difference method." Journal of Computational and Applied Mathematics 198, no. 1 (January 2007): 208–35. http://dx.doi.org/10.1016/j.cam.2005.11.037.

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48

Buhmiler, Sandra, Sanja Rapajić, Slavica Medić, and Tatjana Grbić. "Finite-difference method for singular nonlinear systems." Numerical Algorithms 79, no. 1 (October 19, 2017): 65–86. http://dx.doi.org/10.1007/s11075-017-0428-4.

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49

Lee, C. F., R. T. Shin, and J. A. Kong. "Finite Difference Method for Electromagnetic Scattering Problems." Progress In Electromagnetics Research 04 (1991): 373–442. http://dx.doi.org/10.2528/pier90062700.

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50

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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