Open AccessIntegral equation with the generalized neumann kernel for computing green’s function on simply connected regions
Author(s) -
Ali Hassan Mohamed Murid,
Mohmed M. A. Alagele,
Mohamed M. S. Nasser
Publication year - 2014
Publication title -
malaysian journal of fundamental and applied sciences
Language(s) - English
Resource type - Journals
ISSN - 2289-599X
DOI - 10.11113/mjfas.v9n3.103
Subject(s) - mathematics , fredholm integral equation , integral equation , nyström method , kernel (algebra) , mathematical analysis , summation equation , dirichlet integral , electric field integral equation , poisson kernel , fredholm theory , neumann boundary condition , dirichlet problem , boundary (topology) , boundary value problem , dirichlet's energy , pure mathematics
This research is about computing the Green’s functions on simply connected regions by using the method of boundary integral equation. The method depends on solving a Dirichlet problem 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 numerical method for solving this integral equation is the Nystrӧm method with trapezoidal rule which leads to a system of linear equations. The linear system is then solved by the Gaussian elimination method. Mathematica plot of Green’s function for atest region is also presented.