Green’s Function for Parallel Planes and an Open Rectangular Channel-Flow

Ismail, I. A.; Elbehady, E. E.

doi:10.3390/mca9020215

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Article

1 August 2004

10 Pages

Green’s Function for Parallel Planes and an Open Rectangular Channel-Flow

and

Dean of the faculty of computers and informatics, Zagazig Univ., Zagazig, Egypt

Department of mathematics, faculty of science, Zagazig Univ., Zagazig, Egypt

Author to whom correspondence should be addressed.

Math. Comput. Appl.2004, 9(2), 215-224;https://doi.org/10.3390/mca9020215

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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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