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

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616kB |

Official URL: http://dx.doi.org/10.1155/2022/6488709

## Abstract

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.

Item Type: | Article |
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Uncontrolled Keywords: | Mikhlin’s integral equation, Neumann kernel, Dirichlet boundary |

Subjects: | Q Science > QA Mathematics |

Divisions: | Science |

ID Code: | 104497 |

Deposited By: | Widya Wahid |

Deposited On: | 21 Feb 2024 07:26 |

Last Modified: | 21 Feb 2024 07:26 |

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