Mikhlin's integral equation and the integral equation with the generalized Neumann kernel on simply connected domains
Mikhlin’s integral equation is a classical integral equation for solving boundary value problems for Laplace’s equation. The kernel of the integral equation is known as the Neumann kernel. Recently, an integral equation for solving the Riemann–Hilbert problem was derived. The kernel of the new integ...
Saved in:
| Main Authors: | , , |
|---|---|
| 格式: | Article |
| 语言: | English |
| 出版: |
Hindawi
2022
|
| 主题: | |
| 在线阅读: | http://eprints.utm.my/104497/1/AliHassanMohamed2022_MikhlinsIntegralEquationandtheIntegralEquation.pdf http://eprints.utm.my/104497/ http://dx.doi.org/10.1155/2022/6488709 |
| 标签: |
添加标签
没有标签, 成为第一个标记此记录!
|
| 总结: | Mikhlin’s integral equation is a classical integral equation for solving boundary value problems for Laplace’s equation. The kernel of the integral equation is known as the Neumann kernel. Recently, an integral equation for solving the Riemann–Hilbert problem was derived. The kernel of the new integral equation is a generalization of the Neumann kernel, and hence, it is called the generalized Neumann kernel. The objective of this paper is to present a detailed comparison between these two integral equations with emphasis on their similarities and differences. This comparison is done through applying both equations to solve Laplace’s equation with Dirichlet boundary conditions in simply connected domains with smooth and piecewise smooth boundaries. |
|---|