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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi
2022
|
| Subjects: | |
| Online Access: | http://eprints.utm.my/104497/1/AliHassanMohamed2022_MikhlinsIntegralEquationandtheIntegralEquation.pdf |
| _version_ | 1796867669203353600 |
|---|---|
| author | Naqos, Samir Mohamed Murid, Ali Hassan Nasser, Mohamed M. S. |
| author_facet | Naqos, Samir Mohamed Murid, Ali Hassan Nasser, Mohamed M. S. |
| author_sort | Naqos, Samir |
| collection | ePrints |
| description | 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. |
| first_indexed | 2024-03-05T21:30:45Z |
| format | Article |
| id | utm.eprints-104497 |
| institution | Universiti Teknologi Malaysia - ePrints |
| language | English |
| last_indexed | 2024-03-05T21:30:45Z |
| publishDate | 2022 |
| publisher | Hindawi |
| record_format | dspace |
| spelling | utm.eprints-1044972024-02-21T07:26:19Z http://eprints.utm.my/104497/ Mikhlin's integral equation and the integral equation with the generalized Neumann kernel on simply connected domains Naqos, Samir Mohamed Murid, Ali Hassan Nasser, Mohamed M. S. QA Mathematics 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. Hindawi 2022 Article PeerReviewed application/pdf en http://eprints.utm.my/104497/1/AliHassanMohamed2022_MikhlinsIntegralEquationandtheIntegralEquation.pdf Naqos, Samir and Mohamed Murid, Ali Hassan and Nasser, Mohamed M. S. (2022) Mikhlin's integral equation and the integral equation with the generalized Neumann kernel on simply connected domains. Computational and Mathematical Methods, 2022 (NA). pp. 1-18. ISSN 2577-7408 http://dx.doi.org/10.1155/2022/6488709 DOI : 10.1155/2022/6488709 |
| spellingShingle | QA Mathematics Naqos, Samir Mohamed Murid, Ali Hassan Nasser, Mohamed M. S. Mikhlin's integral equation and the integral equation with the generalized Neumann kernel on simply connected domains |
| title | Mikhlin's integral equation and the integral equation with the generalized Neumann kernel on simply connected domains |
| title_full | Mikhlin's integral equation and the integral equation with the generalized Neumann kernel on simply connected domains |
| title_fullStr | Mikhlin's integral equation and the integral equation with the generalized Neumann kernel on simply connected domains |
| title_full_unstemmed | Mikhlin's integral equation and the integral equation with the generalized Neumann kernel on simply connected domains |
| title_short | Mikhlin's integral equation and the integral equation with the generalized Neumann kernel on simply connected domains |
| title_sort | mikhlin s integral equation and the integral equation with the generalized neumann kernel on simply connected domains |
| topic | QA Mathematics |
| url | http://eprints.utm.my/104497/1/AliHassanMohamed2022_MikhlinsIntegralEquationandtheIntegralEquation.pdf |
| work_keys_str_mv | AT naqossamir mikhlinsintegralequationandtheintegralequationwiththegeneralizedneumannkernelonsimplyconnecteddomains AT mohamedmuridalihassan mikhlinsintegralequationandtheintegralequationwiththegeneralizedneumannkernelonsimplyconnecteddomains AT nassermohamedms mikhlinsintegralequationandtheintegralequationwiththegeneralizedneumannkernelonsimplyconnecteddomains |