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

Siti Zulaiha Aspon | Zendy; Ali H. M. Murid | Zendy; Mohamed M. S. Nasser | Zendy; Hamisan Rahmat | Zendy

Open Access

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

Author(s) -

Siti Zulaiha Aspon,

Ali H. M. Murid,

Mohamed M. S. Nasser,

Hamisan Rahmat

Publication year - 2014

Publication title -

jurnal teknologi

Language(s) - English

Resource type - Journals

eISSN - 2180-3722

pISSN - 0127-9696

DOI - 10.11113/jt.v71.3613

Subject(s) - mathematics , integral equation , fredholm integral equation , nyström method , kernel (algebra) , mathematical analysis , discretization , summation equation , dirichlet integral , dirichlet problem , electric field integral equation , neumann boundary condition , boundary value problem , gauss , dirichlet's principle , pure mathematics , physics , quantum mechanics

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.

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