Integral equation with the generalized neumann kernel for computing green’s function on simply connected regions
DOI:
https://doi.org/10.11113/mjfas.v9n3.103Keywords:
Green’s function, Dirichlet problem, Integral equation, Generalized Neumann kernel,Abstract
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.
References
K. E. Atkinson, The Numerical Solution of Integral Equations of the
Second Kind, Cambridge, Cambridge University Press, 1997.
D. Crowdy, and J. Marshall, IMA J. Appl. Math., 72 (2007) 278-301.
M. Embree, and L. N. Trefethen, SIAM Rev., 41 (1999) 745-761.
J. Helsing, and R. Ojala, J. Comput. Phys., 227 (2008) 2899-2921.
P. Henrici, Applied and Computational Complex Analysis, Vol. 3,
John Wiley, New York, 1986.
A. H. M. Murid, Boundary Integral Equation Approach for Numerical
Conformal Mapping, Ph.D. Thesis, Universiti Teknologi Malaysia,
Skudai, 1997.
M. M. S. Nasser, MATEMATIKA, 23 (2007) 83-98.
R. Wegmann, A. H. M. Murid, and M. M. S. Nasser, J. Comput.
Appl. Math., 182 (2005) 388-415.
