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Regular Papers

High-frequency asymptotics for the modified Helmholtz equation in a quarter-plane

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Pages 1927-1938 | Received 15 Sep 2010, Accepted 21 Oct 2010, Published online: 15 Feb 2011

References

  • Kim , S , Shin , C-S and Keller , JB . 2005 . High-frequency asymptotics for the numerical solution of the Helmholtz equation . Appl. Math. Lett. , 18 : 797 – 804 .
  • Bao , G , Wei , G-W and Zhao , S . 2004 . Numerical solution of the Helmholtz equation with high wavenumbers . Int. J. Numer. Methods. Eng. , 59 : 389 – 408 .
  • Fouassier , E . 2006 . High-frequency analysis of Helmholtz equations: Case of two point sources . SIAM J. Math. Anal. , 38 : 617 – 636 .
  • Giladi , E . 2007 . Asymptotically derived boundary elements for the Helmholtz equation in high frequencies . J. Comput. Appl. Math. , 198 : 52 – 74 .
  • Li , S-H , Lin , W and Sun , M-B . 2008 . A fast collocation method for acoustic scattering in shallow oceans . J. Math. Anal. Appl. , 347 : 607 – 620 .
  • Fokas , AS . 2008 . A Unified Approach to Boundary Value Problems , Philadelphia : SIAM .
  • Berry , MV . 1976 . Waves and Thom's theorem . Adv. Phys. , 25 : 1 – 26 .
  • Berry , MV and Mount , KE . 1972 . Semiclassical approximations in wave mechanics . Rep. Prog. Phys. , 35 : 315 – 397 .
  • Lin , W , Xu , Y and Zhao , YQ . 1996 . Normal modes analysis for sound waves in an ocean with an ice cap and a perfectly reflecting bottom . Appl. Anal. , 63 : 167 – 181 .
  • ben-Avraham , D and Fokas , AS . 1999 . The solution of the modified Helmholtz equation in a wedge and an application to diffusion-limited coalescence . Phys. Lett. A , 263 : 355 – 359 .
  • ben-Avraham , D and Fokas , AS . 2001 . The modified Helmholtz equation in a triangular domain and an application to diffusion-limited coalescence . Phys. Rev. E , 64 016114, pp. 1–6
  • Antipov , YA and Fokas , AS . 2005 . The modified Helmholtz equation in a semi-strip . Math. Proc. Camb. Phil. Soc. , 138 : 339 – 365 .
  • Copson , ET . 1965 . “ Asymptotic Expansions ” . In Cambridge Tracts in Mathematics and Mathematical Physics No. 55 , London : Cambridge University press .
  • Olver , FWJ . 1974 . Asymptotics and Special Functions , New York : Academic Press .
  • Wong , R . 1989 . Asymptotic Approximations of Integrals , Boston : Academic Press .

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