@Article{JCM-19-489,
author = {Tang , Wei-JunFu , Hong-Yuan and Shen , Long-Jun},
title = {The Numerical Solution of First Kind Integral Equation for the Helmholtz Equation on Smooth Open Arcs},
journal = {Journal of Computational Mathematics},
year = {2001},
volume = {19},
number = {5},
pages = {489--500},
abstract = {<p style="text-align: justify;">Consider solving the Dirichlet problem of Helmholtz equation on unbounded region $R^2$\Γ with Γ a smooth open curve in the plane. We use simple-layer potential to construct a solution. This leads to the solution of a logarithmic integral equation of the first kind for the Helmholtz equation. This equation is reformulated using a special change of variable, leading to a new first kind equation with a smooth solution function. This new equation is split into three parts. Then a quadrature method that takes special advantage of the splitting of the integral equation is used to solve the equation numerically. An error analysis in a Sobolev space setting is given. And numerical results show that fast convergence is clearly exhibited. &nbsp;</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/9001.html}
}