A new development of sixth order accurate compact scheme for the Helmholtz equation
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A standard sixth order compact finite difference scheme for two dimensional Helmholtz equation is further improved and a more accurate scheme is presented for the two dimensional Helmholtz equation which is also compact. The novel feature of the present scheme is that it is less sensitive to the associated wave number when compared with that for available sixth order schemes. Theoretical analysis is presented for the newly constructed scheme. The high accuracy of the proposed scheme is illustrated by comparing numerical solutions for solving the two dimensional Helmholtz equations using available sixth-order schemes and the present scheme.
KeywordsFinite difference methods Compact schemes Convergence Helmholtz equations Wave number
Mathematics Subject Classification65N06 65N12 65N15 35J25 65Z05
The authors sincerely thank the editor and anonymous referees for detailed and very helpful suggestions and comments which significantly improved the presentation of this paper. The research work to the first author is supported by SRM Institute of Science and Technology Kattankulathur, Tamil Nadu India. The authors also acknowledge the SERB, New Delhi, India towards computational facility through project file No. MTR/2017/000187. Discussions with Dr. Shuvam Sen is also acknowledged.
- 2.Ames, W.F.: Numerical Methods for Partial Differential Equations. Academic press, Cambridge (2014)Google Scholar
- 19.Peiró, J., Sherwin, S.: Finite difference, finite element and finite volume methods for partial differential equations. In: Yip, S. (ed.) Handbook of materials modeling, 2415–2446. Springer (2005) Google Scholar
- 26.Thomas, J.W.: Numerical Partial Differential Equations: Conservation Laws and Elliptic Equations. Springer, Berlin (2013)Google Scholar
- 29.Young, D.M.: Iterative Solution of Large Linear Systems. Elsevier, Amsterdam (2014)Google Scholar