Study on Vibration of Membranes with Taylor Polynomial Method and Error Analysis for Helmholtz Equation

Ke Yan Wang; Qi Sheng Wang

doi:10.4028/www.scientific.net/AMR.763.234

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HomeAdvanced Materials ResearchAdvanced Materials Research Vol. 763Study on Vibration of Membranes with Taylor...

Study on Vibration of Membranes with Taylor Polynomial Method and Error Analysis for Helmholtz Equation

Abstract:

In this paper, the Taylor polynomial method is used to solve the Helmholtz equation. Using the Taylor polynomial for the method, the Helmholtz equation is transformed into solving matrix equation. The error analysis of this equation is given. A numerical experiment is given to prove the efficiency and dependability of the method.

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Periodical:

Advanced Materials Research (Volume 763)

Pages:

234-237

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.763.234

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Online since:

September 2013

Authors:

Ke Yan Wang, Qi Sheng Wang

Keywords:

Error Analysis, Helmholtz Equation, Taylor Polynomial Method

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References

[1] J.T. Chen, F.C. Wong, Dual formulation of multiple reciprocity method for the acoustic mode of a cavity with a thin partition. J. Sound Vib., 217 (1998) 75–95.

DOI: 10.1006/jsvi.1998.1743

Google Scholar

[2] A.S. Wood, G.E. Tupholme, M.I.H. Bhatti and P.J. Heggs, Steady-state heat transfer through extended plane surfaces, Int. Commun. Heat Mass Transfer, 22 (1995) 99–109.

DOI: 10.1016/0735-1933(94)00056-q

Google Scholar

[3] T. Zhanlav, V. Ulziibayar, The Best Finite-Difference Scheme for the Helmholtz Equation, American Journal of Computational Mathematics, 2 (2012) 207-212.

DOI: 10.4236/ajcm.2012.23026

Google Scholar

[4] S. Amini, S.M. Kirkup, Solution of Helmholtz equation in the exterior domain by elementary boundary integral methods. J. Comput. Phys., 118 (1995) 208-221.

DOI: 10.1006/jcph.1995.1093

Google Scholar

[5] H.W. Zhang, M.X. LI and W.G. Li, Techniques for boundary conditions in point allocation meshless methods, Journal of Dalian University of Technology, 50 (2010) 614-618.

Google Scholar

[6] J. Haslinger, E Neittaanmaki, On different finite element methods for approximating the gradient of the solution to the Helmholtz equation. Comput. Methods Appl. Mech. Engrg., 42 (1984) 131-148.

DOI: 10.1016/0045-7825(84)90022-7

Google Scholar

[7] S. Yalçinbaş, M. Sezer, The approximate solution of the high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials. Applied Mathematics and Computation, 112 (2000) 821-834.

DOI: 10.1016/s0096-3003(99)00059-4

Google Scholar

[8] Q.S. Wang, J.D. Lai, Taylor collocation Solution and Error Analysis for 2-Dimensional Volterra-Fredholm Integral Equations. Journal of Wuyi University (Natural Science Edition), 27 (2013) 1-5 (In Chinese).

Google Scholar