Abstract
In this paper, we consider the modified inhomogeneous Helmholtz equation
Δu(x,y)
Funding statement: This research has been supported by National Foundation of Scientific and Technology Development (Nafosted).
References
[1] Beskos D. E., Boundary element method in dynamic analysis: Part II (1986–1996), ASME Appl. Mech. Rev. 50 (1997), 149–197. 10.1115/1.3101695Search in Google Scholar
[2] Bourgeois L., A mixed formulation of quasi-reversibility to solve the Cauchy problems for Laplace’s equations, Inverse Problems 21 (2005), no. 3, 1087–1104. 10.1088/0266-5611/21/3/018Search in Google Scholar
[3] Chen J. T. and Wong F. C., Dual formulation of multiple reciprocity method for the acoustic mode of a cavity with a thin partition, J. Sound Vibration 217 (1998), 75–95. 10.1006/jsvi.1998.1743Search in Google Scholar
[4] Cheng J., Hon Y. C., Wei T. and Yamamoto M., Numerical computation of a Cauchy problem for Laplace’s equations, ZAMM Z. Angew. Math. Mech. 81 (2001), no. 10, 665–674. 10.1002/1521-4001(200110)81:10<665::AID-ZAMM665>3.0.CO;2-VSearch in Google Scholar
[5] Hall W. S. and Mao X. Q., A boundary element investigation of irregular frequencies in electromagnetic scattering, Eng. Anal. Bound. Elem. 16 (1995), 245–252. 10.1016/0955-7997(95)00068-2Search in Google Scholar
[6] Hao D. N. and Lesnic D., The Cauchy for Laplace’s equation via the conjugate gradient method, IMA J. Appl. Math. 65 (2000), 199–217. 10.1093/imamat/65.2.199Search in Google Scholar
[7] Marin L., Elliott L., Heggs P. J., Ingham D. B., Lesnic D. and Wen X., Conjugate gradient-boundary element solution to the Cauchy problem for Helmholtz-type equations, Comput. Mech. 31 (2003), no. 3–4, 367–377. 10.1007/s00466-003-0439-ySearch in Google Scholar
[8] Marin L., Elliott L., Heggs P. J., Ingham D. B., Lesnic D. and Wen X., BEM solution for the Cauchy problem associated with Helmholtz-type equations by the Landweber method, Eng. Anal. Bound. Elem. 28 (2004), 1025–1034. 10.1016/j.enganabound.2004.03.001Search in Google Scholar
[9] Marin L. and Lesnic D., The method of fundamental solutions for the Cauchy problem associated with two-dimensional Helmholtz-type equations, Comput. Structures 83 (2007), no. 4–5, 267–278. 10.1016/j.compstruc.2004.10.005Search in Google Scholar
[10] Nadukandi P., Oñate E. and García-Espinosa J., Stabilized Finite Element Methods for Convection-Diffusion-Reaction Helmholtz and Stokes Problems, International Center for Numerical Methods in Engineering, Gran Capitan, Barcelona, 2012. Search in Google Scholar
[11] Qian Z., Fu C. L. and Xiong X. T., Fourth order modified method for the Cauchy problem for the Laplace equation, J. Comput. Appl. Math. 192 (2006), 205–218. 10.1016/j.cam.2005.04.031Search in Google Scholar
[12] Shi R., Wei T. and Qin H. H., A fourth-order modified method for the Cauchy problem of the modified Helmholtz equation, Numer. Math. Theory Methods Appl. 2 (2009), 326–340. 10.4208/nmtma.2009.m88032Search in Google Scholar
[13] Vani C. and Avudainayagam A., Regularized solution of the Cauchy problem for the Laplace equation using Meyer wavelets, Math. Comput. Model. 36 (2002), 1151–1159. 10.1016/S0895-7177(02)00265-0Search in Google Scholar
[14] Wood A. S., Tupholme G. E., Bhatti M. I. H. and Heggs P. J., Steady-state heat transfer through extended plane surfaces, Int. Comm. Heat Mass Transf. 22 (1995), 99–109. 10.1016/0735-1933(94)00056-QSearch in Google Scholar
[15] Xiong X., Shi W. and Fan X., Two numerical methods for a Cauchy problem for modified Helmholtz equation, Appl. Math. Modell. 35 (2011), 4951–4964. 10.1016/j.apm.2011.04.001Search in Google Scholar
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