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Journal articles on the topic 'Elliptic method'

Author: Grafiati

Published: 28 June 2021

Last updated: 1 February 2022

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1

Yin, Zhen, Hua Li, Zi Yang Cao, Ou Xie, and Yan Li. "Simulation and Experiment of New Longitudinal-Torsional Composite Ultrasonic Elliptical Vibrator." Advanced Materials Research 338 (September 2011): 79–83. http://dx.doi.org/10.4028/www.scientific.net/amr.338.79.

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A new ultrasonic elliptic vibrator design method was proposed, the ultrasonic elliptic vibration was achieved by the structural curve of the longitudinal and torsional vibrations. The model, harmonic and transient analyses of the new longitudinal-torsional composite ultrasonic elliptical vibrator were performed by using the software ANSYS, the prototype of the new vibrator was tested by using impedance analyzer and PSV-400 laser Doppler vibrometer, the correctness of the finite element simulation results and the feasibility of the new longitudinal-torsional composite ultrasonic elliptical vibrator design methods were verified.

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2

Yin, Zhen, Hua Li, Bang Fu Wang, and Ke Feng Song. "Study on the Design of Longitudinal-Torsional Composite Ultrasonic Elliptical Vibrator Based on FEM." Advanced Materials Research 308-310 (August 2011): 341–45. http://dx.doi.org/10.4028/www.scientific.net/amr.308-310.341.

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Based on FEM, a new type of ultrasonic elliptic vibrator design method was proposed, the ultrasonic elliptic vibration was achieved by the structural curve of the longitudinal and torsional vibrations. The impedance and vibration characteristics of the new longitudinal-torsional composite ultrasonic elliptic vibrator prototype were tested. It provides an important basis for impedance matching and longitudinal-torsional composite ultrasonic elliptical vibration application.

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3

Noguchi, Tetsuo, and Tsutomu Ezumi. "OS01W0062 A study about the elliptic inclusion by optical method and finite element method." Abstracts of ATEM : International Conference on Advanced Technology in Experimental Mechanics : Asian Conference on Experimental Mechanics 2003.2 (2003): _OS01W0062. http://dx.doi.org/10.1299/jsmeatem.2003.2._os01w0062.

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4

AIKAWA, Yusuke, Koji NUIDA, and Masaaki SHIRASE. "Elliptic Curve Method Using Complex Multiplication Method." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E102.A, no. 1 (January 1, 2019): 74–80. http://dx.doi.org/10.1587/transfun.e102.a.74.

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5

Tanaka, Naoyuki. "A New Calculation Method of Hertz Elliptical Contact Pressure." Journal of Tribology 123, no. 4 (December 7, 2000): 887–89. http://dx.doi.org/10.1115/1.1352745.

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A new method for calculating elliptical Hertz contact pressure in which an elliptic integral is not necessary, has been developed. The simplest numerical integration by this method yields a Hertz contact pressure within 0.0005 percent of the theoretical spherical contact pressure. And dimensionless quantities, for calculating contact pressure, major and minor semi-axes and approach calculated by using the method agree well with those given in the references. Elliptical Hertz contact pressure can thus now be calculated by using a spreadsheet program for personal computers.

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6

Elías-Zúñiga, Alex. "On The Elliptic Balance Method." Mathematics and Mechanics of Solids 8, no. 3 (June 2003): 263–79. http://dx.doi.org/10.1177/1081286503008003002.

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7

Jingzhi Li, Shanqiang Li, and Hongyu Liu. "RESTARTED NONLINEAR CONJUGATE GRADIENT METHOD FOR PARAMETER IDENTIFICATION IN ELLIPTIC SYSTEM." Eurasian Journal of Mathematical and Computer Applications 1, no. 1 (2013): 62–77. http://dx.doi.org/10.32523/2306-3172-2013-1-1-62-77.

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8

ZHAO, HONG. "ANALYTICAL STUDY ON NONLINEAR DIFFERENTIAL–DIFFERENCE EQUATIONS VIA A NEW METHOD." Modern Physics Letters B 24, no. 08 (March 30, 2010): 761–73. http://dx.doi.org/10.1142/s0217984910022846.

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Based on the computerized symbolic computation, a new rational expansion method using the Jacobian elliptic function was presented by means of a new general ansätz and the relations among the Jacobian elliptic functions. The results demonstrated an effective direction in terms of a uniformed construction of the new exact periodic solutions for nonlinear differential–difference equations, where two representative examples were chosen to illustrate the applications. Various periodic wave solutions, including Jacobian elliptic sine function, Jacobian elliptic cosine function and the third elliptic function solutions, were obtained. Furthermore, the solitonic solutions and trigonometric function solutions were also obtained within the limit conditions in this paper.

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9

Hlaváček, Ivan. "Domain optimization in $3D$-axisymmetric elliptic problems by dual finite element method." Applications of Mathematics 35, no. 3 (1990): 225–36. http://dx.doi.org/10.21136/am.1990.104407.

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10

Hlaváček, Ivan. "Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions." Applications of Mathematics 35, no. 5 (1990): 405–17. http://dx.doi.org/10.21136/am.1990.104420.

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11

Blaheta, Radim. "A multilevel method with correction by aggregation for solving discrete elliptic problems." Applications of Mathematics 31, no. 5 (1986): 365–78. http://dx.doi.org/10.21136/am.1986.104214.

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12

Zhang, Li, Guo Jun Dai, and Chang Jun Wang. "Human Tracking Method Based on Maximally Stable Extremal Regions with Multi-Cameras." Applied Mechanics and Materials 44-47 (December 2010): 3681–86. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.3681.

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With respect to the human tracking with multi-cameras in the video surveillance system, a human tracking method based on MSER (Maximally Stable Extremal Regions) was established. The approach transforms the human tracking into elliptic region matching. The method does elliptic region fitting to each MSER, and then selects the elliptic regions which meet some constraints. These selected elliptic regions are normalized to unity circular regions. The right matched elliptic regions are gotten by rotational invariant vectors calculation, histogram density estimation and weighted average distance calculation. Experimental results show that the approach can effectively realize the human tracking with multi-cameras.

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13

Kozevnikov, V. A., and V. E. Privalov. "The laser gain under nonhomogeneous boundary conditions." Izvestiya vysshikh uchebnykh zavedenii. Fizika, no. 9 (2020): 165–71. http://dx.doi.org/10.17223/00213411/63/9/165.

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The method proposed by the authors for solving the Helmholtz equation with homogeneous boundary conditions was tested for an elliptic section. The method is generalized to the Helmholtz equation with inhomogeneous boundary conditions. The generalization is verified for circular and elliptical sections.

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14

Huang, Jing Zhi, Teng Hui Guo, Jiu Bin Tan, and Tao Sun. "Dynamic Calibration for Measurement System of Form Measuring Instruments Based on Elliptical Standard." Applied Mechanics and Materials 870 (September 2017): 203–8. http://dx.doi.org/10.4028/www.scientific.net/amm.870.203.

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A dynamic calibration method based on elliptical standard was put forward to further improve the calibration repeatability of measurement system of form measuring instruments. In this method, the radius difference of the major axis to the minor axis of elliptic contour acts as the standard value to calibrate the measuring system, and a low pass filter is used to filter the roughness, electrical noise and high frequency vibration signal which mixed into measurement data, the elliptic contour feature can be obtained accurately based on the low order harmonic properties. Compared with the traditional calibration method of flick standard, the proposed method ensure the calibration state is well consistent with the normal measuring state of the measuring system. Experimental results indicate that the calibration repeatability with 10nm can be achieved by measuring an elliptical standard. This method has been used in the calibration of measurement system of self-made ultra-precision cylindricity measuring instrument.

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15

Kaplan, A., and R. Tichatschke. "Proximal point method and elliptic regularization." Nonlinear Analysis: Theory, Methods & Applications 71, no. 10 (November 2009): 4525–43. http://dx.doi.org/10.1016/j.na.2009.03.010.

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16

Liu, Xiang-Qing, Jia-Quan Liu, and Zhi-Qiang Wang. "Quasilinear elliptic equations via perturbation method." Proceedings of the American Mathematical Society 141, no. 1 (May 9, 2012): 253–63. http://dx.doi.org/10.1090/s0002-9939-2012-11293-6.

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17

Khalid, M., and K. A. Juhany. "An expression for the dynamic stability of blunt slender elliptic bodies in hypersonic flow." Aeronautical Journal 118, no. 1207 (September 2014): 1079–89. http://dx.doi.org/10.1017/s0001924000009751.

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AbstractDynamic stability data on axially symmetric pointed and blunt cones, parabolic profiles and other ogive and blunt cylindrical shapes is readily available in literature; the dynamic stability on elliptic blunt paraboloids has not been studied at any great lengths in the past. Both numerical and experimental results are scarce. The present paper uses the shock expansion method to obtain the unsteady pressure distribution on blunt elliptic conical bodies at small angles-of-attack. The resulting unsteady pressure distribution is suitably integrated over the surface of the elliptic body to obtain appropriate analytic expressions for static and dynamic stability. Owing to scarcity of meaningful numerical or measured data for elliptic bodies, the results are compared in qualitative terms against published dynamic stability data on pointed elliptical cones or other axisymmetric blunt cones.

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18

Yang, Zonghang, and Benny Y. C. Hon. "An Improved Modified Extended tanh-Function Method." Zeitschrift für Naturforschung A 61, no. 3-4 (April 1, 2006): 103–15. http://dx.doi.org/10.1515/zna-2006-3-401.

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In this paper we further improve the modified extended tanh-function method to obtain new exact solutions for nonlinear partial differential equations. Numerical applications of the proposed method are verified by solving the improved Boussinesq equation and the system of variant Boussinesq equations. The new exact solutions for these equations include Jacobi elliptic doubly periodic type,Weierstrass elliptic doubly periodic type, triangular type and solitary wave solutions

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19

Antonietti, Paola F., Blanca Ayuso de Dios, Susanne C. Brenner, and Li-yeng Sung. "Schwarz Methods for a Preconditioned WOPSIP Method for Elliptic Problems." Computational Methods in Applied Mathematics 12, no. 3 (2012): 241–72. http://dx.doi.org/10.2478/cmam-2012-0021.

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Abstract We propose and analyze several two-level non-overlapping Schwarz methods for a preconditioned weakly over-penalized symmetric interior penalty (WOPSIP) discretization of a second order boundary value problem. We show that the preconditioners are scalable and that the condition number of the resulting preconditioned linear systems of equations is independent of the penalty parameter and is of order H/h, where H and h represent the mesh sizes of the coarse and fine partitions, respectively. Numerical experiments that illustrate the performance of the proposed two-level Schwarz methods are also presented.

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20

Mokin, Yu I. "The capacitance matrix method in numerical methods for elliptic equations." USSR Computational Mathematics and Mathematical Physics 26, no. 6 (January 1986): 199–200. http://dx.doi.org/10.1016/0041-5553(86)90171-0.

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21

Hlaváček, Ivan. "Optimization of the domain in elliptic problems by the dual finite element method." Applications of Mathematics 30, no. 1 (1985): 50–72. http://dx.doi.org/10.21136/am.1985.104126.

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22

Zhang, Li Hong, and Shu Qian Chen. "Implementation of Embedded Mobile Device Elliptic Curve Algorithm Fast Generating Algorithm." Advanced Materials Research 694-697 (May 2013): 2599–603. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.2599.

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Elliptic curve cryptosystem is used in the process of embedded systems, the selection and generation algorithm of the elliptic curve will directly affect the efficiency of systems. From Elliptic Curve's selection, Elliptic Curve's structure, Elliptic Curve's generation, this paper discussed the realization of a random elliptic curve method of Embedded Mobile Device, the SEA algorithm and its improved algorithm. The results show that this method can achieve a quick implementation of the elliptic curve method to improve the operating efficiency of embedded systems in the same security guarantees.

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23

Amir, Supri Bin Hj, and Bagas Prasetyo. "Comparison of Elliptic Envelope Method and Isolation Forest Method on Imbalance Dataset." Jurnal Matematika, Statistika dan Komputasi 17, no. 1 (August 24, 2020): 42–49. http://dx.doi.org/10.20956/jmsk.v17i1.10899.

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The problem of unbalanced data is important in the field of Data Mining. Dataset with unbalanced classes is a dataset whose frequency of occurrence of certain classes is very much different from other classes. This imbalance problem will bias the classifier's performance. Many researchers have examined both the development of algorithms and modifications to the preprocessing stage to overcome this problem. This study discusses the comparison of One Class Classification algorithms, namely Elliptic Envelope and Isolation Forest on unbalanced data. From this study, the Elliptic Envelope Method showed better results compared to the Isolation Forest method with 80.28% recall testing and 80.28% precision while Isolation Forest showed 46.95% recall results and 46.95% precision.

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24

Skuratovskii, Ruslan, and Volodymyr Osadchyy. "Elliptic and Edwards Curves Order Counting Method." International Journal of Mathematical Models and Methods in Applied Sciences 15 (April 5, 2021): 52–62. http://dx.doi.org/10.46300/9101.2021.15.8.

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We consider the algebraic affine and projective curves of Edwards over the finite field Fpn. It is well known that many modern cryptosystems can be naturally transformed into elliptic curves. In this paper, we extend our previous research into those Edwards algebraic curves over a finite field. We propose a novel effective method of point counting for both Edwards and elliptic curves. In addition to finding a specific set of coefficients with corresponding field characteristics for which these curves are supersingular, we also find a general formula by which one can determine whether or not a curve Ed[Fp] is supersingular over this field. The method proposed has complexity O ( p log2 2 p ) . This is an improvement over both Schoof’s basic algorithm and the variant which makes use of fast arithmetic (suitable for only the Elkis or Atkin primes numbers) with complexities O(log8 2 pn) and O(log4 2 pn) respectively. The embedding degree of the supersingular curve of Edwards over Fpn in a finite field is additionally investigated. Due existing the birational isomorphism between twisted Edwards curve and elliptic curve in Weierstrass normal form the result about order of curve over finite field is extended on cubic in Weierstrass normal form.

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25

Hu, Jian Jun. "Constructing Elliptic Curves over Ramanujan's Class Invariants." Advanced Materials Research 915-916 (April 2014): 1336–40. http://dx.doi.org/10.4028/www.scientific.net/amr.915-916.1336.

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The Complex Multiplication (CM) method is a widely used technique for constructing elliptic curves over finite fields. The key point in this method is parameter generation of the elliptic curve and root compution of a special type of class polynomials. However, there are several class polynomials which can be used in the CM method, having much smaller coefficients, and fulfilling the prerequisite that their roots can be easily transformed to the roots of the corresponding Hilbert polynomials.In this paper, we provide a method which can construct elliptic curves by Ramanujan's class invariants. We described the algorithm for the construction of elliptic curves (ECs) over imaginary quadratic field and given the transformation from their roots to the roots of the corresponding Hilbert polynomials. We compared the efficiency in the use of this method and other methods.

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26

Stroeker, Roel J., and Nikos Tzanakis. "On the Elliptic Logarithm Method for Elliptic Diophantine Equations: Reflections and an Improvement." Experimental Mathematics 8, no. 2 (January 1999): 135–49. http://dx.doi.org/10.1080/10586458.1999.10504395.

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27

OKABE, Tadashi, Takahiro KONDOU, and Hirofumi WATANABE. "An Elliptic Averaging Method Using Sum of Jacobian Elliptic Cosine and Sine Functions." Transactions of the Japan Society of Mechanical Engineers Series C 74, no. 744 (2008): 1971–78. http://dx.doi.org/10.1299/kikaic.74.1971.

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28

Zhang, Lihong, Shuqian Chen, and Yanglie Fu. "Fast Elliptic Curve Algorithm of Embedded Mobile Equipment." Open Electrical & Electronic Engineering Journal 7, no. 1 (December 13, 2013): 138–42. http://dx.doi.org/10.2174/1874129001307010138.

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Selection Algorithm and Generation Algorithm of elliptic curves have been the focus of research and hotspot of the Elliptic Curve Cryptosystem. This paper discusses a random elliptic curve realization method of Embedded Mobile Equipment, the SEA algorithm and its improved algorithm from Elliptic Curve's selection, Elliptic Curve's structure and Elliptic Curve's generation. Ensuring that the embedded system in the security situation goes through invariable situation causes the embedded system to realize a fast elliptic curve realization method, which enhances the efficiency of embedded system.

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29

Zhukov, V. T., N. D. Novikova, and O. B. Feodoritova. "Parallel multigrid method for solving elliptic equations." Mathematical Models and Computer Simulations 6, no. 4 (July 2014): 425–34. http://dx.doi.org/10.1134/s2070048214040103.

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30

Cangiani, A., P. Chatzipantelidis, G. Diwan, and E. H. Georgoulis. "Virtual element method for quasilinear elliptic problems." IMA Journal of Numerical Analysis 40, no. 4 (July 4, 2019): 2450–72. http://dx.doi.org/10.1093/imanum/drz035.

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Abstract A virtual element method for the quasilinear equation $-\textrm{div} ({\boldsymbol \kappa }(u)\operatorname{grad} u)=f$ using general polygonal and polyhedral meshes is presented and analysed. The nonlinear coefficient is evaluated with the piecewise polynomial projection of the virtual element ansatz. Well posedness of the discrete problem and optimal-order a priori error estimates in the $H^1$- and $L^2$-norm are proven. In addition, the convergence of fixed-point iterations for the resulting nonlinear system is established. Numerical tests confirm the optimal convergence properties of the method on general meshes.

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31

Jin, Zhiren. "A truncation method for semilinear elliptic equations." Communications in Partial Differential Equations 19, no. 3-4 (January 1994): 605–16. http://dx.doi.org/10.1080/03605309408821026.

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32

HUN, Sang, and Byeong CHUN. "Preconditioning cubic collocation method for elliptic equations." Hokkaido Mathematical Journal 26, no. 3 (February 1997): 597–610. http://dx.doi.org/10.14492/hokmj/1351258267.

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33

Xu, Fei, Hongkun Ma, and Jian Zhai. "Multigrid method for coupled semilinear elliptic equation." Mathematical Methods in the Applied Sciences 42, no. 8 (March 3, 2019): 2707–20. http://dx.doi.org/10.1002/mma.5543.

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34

Cai, Zhiqiang, and E. Weinan. "Hierarchical method for elliptic problems using wavelet." Communications in Applied Numerical Methods 8, no. 11 (November 1992): 819–25. http://dx.doi.org/10.1002/cnm.1630081105.

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35

Löhner, R., and K. Morgan. "An unstructured multigrid method for elliptic problems." International Journal for Numerical Methods in Engineering 24, no. 1 (January 1987): 101–15. http://dx.doi.org/10.1002/nme.1620240108.

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36

Bravo Yuste, S. "The Rayleigh method with Jacobi elliptic functions." Journal of Sound and Vibration 133, no. 1 (August 1989): 180–84. http://dx.doi.org/10.1016/0022-460x(89)90993-0.

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37

MATSUNO, Kenichi. "Solution-Adaptive Grid Method Using Elliptic Equation." Journal of the Japan Society for Aeronautical and Space Sciences 43, no. 492 (1995): 26–31. http://dx.doi.org/10.2322/jjsass1969.43.26.

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38

Chen, Huaitang, and Huicheng Yin. "A note on the elliptic equation method." Communications in Nonlinear Science and Numerical Simulation 13, no. 3 (June 2008): 547–53. http://dx.doi.org/10.1016/j.cnsns.2006.06.007.

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39

El-Sabbagh, M. F., and A. T. Ali. "New generalized Jacobi elliptic function expansion method." Communications in Nonlinear Science and Numerical Simulation 13, no. 9 (November 2008): 1758–66. http://dx.doi.org/10.1016/j.cnsns.2007.04.014.

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40

Schaeffer, Hayden, and Thomas Y. Hou. "An Accelerated Method for Nonlinear Elliptic PDE." Journal of Scientific Computing 69, no. 2 (May 12, 2016): 556–80. http://dx.doi.org/10.1007/s10915-016-0215-8.

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41

Xia, Kelin, Meng Zhan, and Guo-Wei Wei. "MIB Galerkin method for elliptic interface problems." Journal of Computational and Applied Mathematics 272 (December 2014): 195–220. http://dx.doi.org/10.1016/j.cam.2014.05.014.

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42

Atkinson, Kendall, David Chien, and Olaf Hansen. "A spectral method for nonlinear elliptic equations." Numerical Algorithms 74, no. 3 (July 16, 2016): 797–819. http://dx.doi.org/10.1007/s11075-016-0172-1.

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43

Chen, Peimin, Walter Allegretto, and Yanping Lin. "A multiscale method for semilinear elliptic equations." Journal of Mathematical Analysis and Applications 345, no. 1 (September 2008): 362–71. http://dx.doi.org/10.1016/j.jmaa.2008.03.069.

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44

Hyon, Yun K., Ho J. Jang, and Do Y. Kwak. "A nonconforming covolume method for elliptic problems." Applied Mathematics and Computation 196, no. 1 (February 2008): 60–66. http://dx.doi.org/10.1016/j.amc.2007.05.036.

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45

Bornemann, Folkmar A., and Peter Deuflhard. "The cascadic multigrid method for elliptic problems." Numerische Mathematik 75, no. 2 (December 1, 1996): 135–52. http://dx.doi.org/10.1007/s002110050234.

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46

Xue, Jin Xue, and Bo Zhao. "Research on Grinding Temperature of Nano Z_rO₂ Ceramics Using Diamond Grinding Wheel Dressed by Elliptic Ultrasonic Vibration." Applied Mechanics and Materials 42 (November 2010): 313–16. http://dx.doi.org/10.4028/www.scientific.net/amm.42.313.

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In order to investigate the influence of dressing methods on grinding temperature, two kinds of diamond grinding wheels dressed by traditional dressing(TD) and elliptic ultrasonic vibration dressing(ED) respectively were used to grind the same nano-ceramic material. Through grinding experiments, the comparative analysis of the grinding temperature was conducted. The results show that diamond grinding wheel dressed by elliptical ultrasonic vibration method can decrease the grinding temperature.

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47

Pallikaris, Athanasios, and George Latsas. "New Algorithm for Great Elliptic Sailing (GES)." Journal of Navigation 62, no. 3 (June 15, 2009): 493–507. http://dx.doi.org/10.1017/s0373463309005323.

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An analytical method and algorithm for great elliptic sailing (GES) calculations is presented. The method solves the complete GES problem calculating not only the great elliptic arc distance, but also other elements of the sailing such as the geodetic coordinates of intermediate points along the great elliptic arc. The proposed formulas provide extremely high accuracies and are straightforward to be exploited immediately in the development of navigational software, without the requirement to use advanced numerical methods. Their validity and effectiveness have been verified with numerical tests and comparisons to extremely accurate geodetic methods for the direct and inverse geodetic problem.

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48

Gepreel, Khaled A., and Amr M. S. Mahdy. "Algebraic computational methods for solving three nonlinear vital models fractional in mathematical physics." Open Physics 19, no. 1 (January 1, 2021): 152–69. http://dx.doi.org/10.1515/phys-2021-0020.

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Abstract This research paper uses a direct algebraic computational scheme to construct the Jacobi elliptic solutions based on the conformal fractional derivatives for nonlinear partial fractional differential equations (NPFDEs). Three vital models in mathematical physics [the space-time fractional coupled Hirota Satsuma KdV equations, the space-time fractional symmetric regularized long wave (SRLW equation), and the space-time fractional coupled Sakharov–Kuznetsov (S–K) equations] are investigated through the direct algebraic method for more explanation of their novel characterizes. This approach is an easy and powerful way to find elliptical Jacobi solutions to NPFDEs. The hyperbolic function solutions and trigonometric functions where the modulus and, respectively, are degenerated by Jacobi elliptic solutions. In this style, we get many different kinds of traveling wave solutions such as rational wave traveling solutions, periodic, soliton solutions, and Jacobi elliptic solutions to nonlinear evolution equations in mathematical physics. With the suggested method, we were fit to find much explicit wave solutions of nonlinear integral differential equations next converting them into a differential equation. We do the 3D and 2D figures to define the kinds of outcome solutions. This style is moving, reliable, powerful, and easy for solving more difficult nonlinear physics mathematically.

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49

Chen, Yong, Qi Wang, and Biao Lic. "Jacobi Elliptic Function Rational Expansion Method with Symbolic Computation to Construct New Doubly-periodic Solutions of Nonlinear Evolution Equations." Zeitschrift für Naturforschung A 59, no. 9 (September 1, 2004): 529–36. http://dx.doi.org/10.1515/zna-2004-0901.

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A new Jacobi elliptic function rational expansion method is presented by means of a new general ansatz and is very powerful, with aid of symbolic computation, to uniformly construct more new exact doubly-periodic solutions in terms of rational form Jacobi elliptic function of nonlinear evolution equations (NLEEs). We choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we obtain the solutions found by most existing Jacobi elliptic function expansion methods and find other new and more general solutions at the same time. When the modulus of the Jacobi elliptic functions m→1 or 0, the corresponding solitary wave solutions and trigonometric function (singly periodic) solutions are also found.

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50

Wang, Qiuliang, and Jinru Chen. "An Unfitted Discontinuous Galerkin Method for Elliptic Interface Problems." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/241890.

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An unfitted discontinuous Galerkin method is proposed for the elliptic interface problems. Based on a variant of the local discontinuous Galerkin method, we obtain the optimal convergence for the exact solutionuin the energy norm and its fluxpin theL2norm. These results are the same as those in the case of elliptic problems without interface. Finally, some numerical experiments are presented to verify our theoretical results.

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