Integral Equation Approach for Computing Green’s Function on Doubly Connected Regions via the Generalized Neumann Kernel

Authors

  • Siti Zulaiha Aspon Department of Mathematical Sciences, Faculty of Science, UTM, 81310 UTM Johor Bahru, Johor, Malaysia
  • Ali Hassan Mohamed Murid UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), 81310 UTM Johor Bahru, Johor, Malaysia
  • Mohamed M. S. Nasser Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia
  • Hamisan Rahmat Department of Mathematical Sciences, Faculty of Science, UTM, 81310 UTM Johor Bahru, Johor, Malaysia

DOI:

https://doi.org/10.11113/jt.v71.3613

Keywords:

Green’s Function, Dirichlet Problem, Integral Equation, Generalized Neumann Kernel

Abstract

This research is about computing the Green’s function on doubly connected regions by using the method of boundary integral equation. The method depends on solving a Dirichlet problem. The Dirichlet problem is then solved using a uniquely solvable Fredholm integral equation on the boundary of the region. The kernel of this integral equation is the generalized Neumann kernel. The method for solving this integral equation is by using the Nystrӧm method with trapezoidal rule to discretize it to a linear system. The linear system is then solved by the Gauss elimination method. Mathematica plots of Green’s functions for several test regions are also presented.

References

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Published

2014-10-27

Issue

Vol. 71 No. 1: November 2014

Section

Science and Engineering

License

Copyright of articles that appear in Jurnal Teknologi belongs exclusively to Penerbit Universiti Teknologi Malaysia (Penerbit UTM Press). This copyright covers the rights to reproduce the article, including reprints, electronic reproductions, or any other reproductions of similar nature.

How to Cite

Integral Equation Approach for Computing Green’s Function on Doubly Connected Regions via the Generalized Neumann Kernel. (2014). Jurnal Teknologi, 71(1). https://doi.org/10.11113/jt.v71.3613