Author/Authors :
Aspon, Siti Zulaiha Universiti Teknologi Malaysia (UTM) - Faculty of Science - Department of Mathematical Sciences, Malaysia , Murid, Ali Hassan Mohamed Universiti Teknologi Malaysia (UTM) - Faculty of Science, UTM Centre for Industrial and Applied Mathematics - Department of Mathematical Sciences, Malaysia , Nasser, Mohamed M. S. King Khalid University - Faculty of Science - Department of Mathematics, Saudi Arabia , Rahmat, Hamisan Universiti Teknologi Malaysia(UTM) - Faculty of Science - Department of Mathematical Sciences, Malaysia
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.
Keywords :
Green’s Function , Dirichlet Problem , Integral Equation , Generalized Neumann Kernel
