{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:08:51Z","timestamp":1740103731278,"version":"3.37.3"},"reference-count":22,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,1,20]],"date-time":"2020-01-20T00:00:00Z","timestamp":1579478400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11661005","11301070","YJRC2018-1","CS18ZDZ02"],"award-info":[{"award-number":["11661005","11301070","YJRC2018-1","CS18ZDZ02"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11661005","11301070","YJRC2018-1","CS18ZDZ02"],"award-info":[{"award-number":["11661005","11301070","YJRC2018-1","CS18ZDZ02"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004498","name":"Chengdu Normal University","doi-asserted-by":"publisher","award":["11661005","11301070","YJRC2018-1","CS18ZDZ02"],"award-info":[{"award-number":["11661005","11301070","YJRC2018-1","CS18ZDZ02"]}],"id":[{"id":"10.13039\/501100004498","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004498","name":"Chengdu Normal University","doi-asserted-by":"publisher","award":["11661005","11301070","YJRC2018-1","CS18ZDZ02"],"award-info":[{"award-number":["11661005","11301070","YJRC2018-1","CS18ZDZ02"]}],"id":[{"id":"10.13039\/501100004498","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,1,20]]},"abstract":"<jats:p>In this paper, we derive the convergence for the high-accuracy algorithm in solving the Dirichlet problem of the modified Helmholtz equation. By the boundary element method, we transform the system to be a boundary integral equation. The high-accuracy algorithm using the specific quadrature rule is developed to deal with weakly singular integrals. The convergence of the algorithm is proved based on Anselone\u2019s collective compact theory. Moreover, an asymptotic error expansion shows that the algorithm is of order <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>O<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>h<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><mml:mrow><mml:mn>3<\/mml:mn><\/mml:mrow><\/mml:msubsup><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:math>. The numerical examples support the theoretical analysis.<\/jats:p>","DOI":"10.1155\/2020\/6484890","type":"journal-article","created":{"date-parts":[[2020,1,20]],"date-time":"2020-01-20T18:38:06Z","timestamp":1579545486000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["Convergence of the High-Accuracy Algorithm for Solving the Dirichlet Problem of the Modified Helmholtz Equation"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8624-8792","authenticated-orcid":true,"given":"Hu","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics, Chengdu Normal University, Chengdu 611130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1324-7734","authenticated-orcid":true,"given":"Guang","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Sciences, East China University of Technology, Nanchang 330013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-003-0439-y"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1115\/1.3101695"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2005.06.006"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1137\/s1064827597317648"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2019.01.035"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.4208\/aamm.oa-2018-0103"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2019.124658"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2019.112729"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.enganabound.2015.10.007"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2015.05.017"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2019.06.010"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2014.02.010"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2010.09.030"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-014-9975-1"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1216\/jie-1988-1-4-549"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1090\/s0025-5718-1990-0995213-6"},{"first-page":"359","volume-title":"A new variable transformation for numerical integration","year":"1993","key":"17"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/8.1.105"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1007\/bf01061258"},{"year":"1984","key":"20"},{"issue":"1","key":"21","first-page":"9","volume":"24","year":"2006","journal-title":"Journal of Computational Mathematics"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-012-9563-0"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/6484890.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/6484890.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/6484890.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,20]],"date-time":"2020-01-20T18:38:10Z","timestamp":1579545490000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/6484890\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,20]]},"references-count":22,"alternative-id":["6484890","6484890"],"URL":"https:\/\/doi.org\/10.1155\/2020\/6484890","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2020,1,20]]}}}