Many examples are herein given and discussed for the numerical applications of the above two cases; and then we make a comparison between our calculations and some others.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Here we use a more convenient technique to generate a faster convergent Green's function needed for solving Laplace's equation in two cases: the first domain is bounded by two parallel planes; and the second is an infinite open rectangular prism.
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Temel Bulgular & Veri:Green's function usually is expressed as a series of images which is slowly convergent, and that is why we transform it into an integral representation which is rapidly convergent and stable.
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Sonuç & Katkı:Many examples are herein given and discussed for the numerical applications of the above two cases; and then we make a comparison between our calculations and some others.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
Here we use a more convenient technique to generate a faster convergent Green's function needed for solving Laplace's equation in two cases: the first domain is bounded by two parallel planes; and the second is an infinite open rectangular prism. Green's function usually is expressed as a series of images which is slowly convergent, and that is why we transform it into an integral representation which is rapidly convergent and stable. Many examples are herein given and discussed for the numerical applications of the above two cases; and then we make a comparison between our calculations and some others.
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Bu Makaleye Atıf Yap
ISMAIL, I. A., ELBEHADY, E. (2004). Green's function for parallel planes and an open rectangular channel-flow. Mathematical and Computational Applications, Cilt: 9 - Sayı: 2, 215–224. https://ajindex.com/articles/280138
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Second Edition,
Cambridge, London, New York, 1981. 5.S. R. Breit, The potential of a Rankine source between parallel planes and in a rectangular cylinder. J. Eng. Math. 25,151-163,1991. 6.J. J. Tuma and R. A. Walsh, Engineering Mathematics Handbook, McGraw-Hill, Forth Edition, 1998. 7.J. N. Newman, The Green function for potential flow in a rectangular channel, J. Eng.Math. 26,51-59,1992. 8.C. L. Linton, The Green's function for the two-dimensional Helmholtz equation in periodic domains. J. Eng. Math. 33, 377-402,1998. 9.R. Piessens and et al, QUADPACK-A Subroutine package for automatic integration, Springer-Verlag, Berlin, 1983. 10.G. D. Smith, Numerical Solution of Partial Differential Equations, Oxford University Press, Oxford, 1985.