{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T23:39:12Z","timestamp":1740181152587,"version":"3.37.3"},"reference-count":34,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,4,20]],"date-time":"2022-04-20T00:00:00Z","timestamp":1650412800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002385","name":"Ministry of Higher Education","doi-asserted-by":"publisher","award":["FRGS\/1\/2019\/STG06\/UTM\/02\/20"],"award-info":[{"award-number":["FRGS\/1\/2019\/STG06\/UTM\/02\/20"]}],"id":[{"id":"10.13039\/501100002385","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005417","name":"Universiti Teknologi Malaysia","doi-asserted-by":"publisher","award":["FRGS\/1\/2019\/STG06\/UTM\/02\/20"],"award-info":[{"award-number":["FRGS\/1\/2019\/STG06\/UTM\/02\/20"]}],"id":[{"id":"10.13039\/501100005417","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods"],"published-print":{"date-parts":[[2022,4,20]]},"abstract":"<jats:p>Mikhlin\u2019s integral equation is a classical integral equation for solving boundary value problems for Laplace\u2019s equation. The kernel of the integral equation is known as the Neumann kernel. Recently, an integral equation for solving the Riemann\u2013Hilbert 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\u2019s equation with Dirichlet boundary conditions in simply connected domains with smooth and piecewise smooth boundaries.<\/jats:p>","DOI":"10.1155\/2022\/6488709","type":"journal-article","created":{"date-parts":[[2022,4,20]],"date-time":"2022-04-20T17:05:13Z","timestamp":1650474313000},"page":"1-18","source":"Crossref","is-referenced-by-count":0,"title":["Mikhlin\u2019s Integral Equation and the Integral Equation with the Generalized Neumann Kernel on Simply Connected Domains"],"prefix":"10.1155","volume":"2022","author":[{"given":"Samir","family":"Naqos","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9843-228X","authenticated-orcid":true,"given":"Ali H. 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