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By discrete energy method, the proposed difference scheme is proven to be of second-order convergence and of unconditional stability with respect to both initial conditions and right-hand term in a proper discretized <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:msup><mml:mrow><mml:mi>L<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:math> norm. The theoretical result is verified by a numerical experiment.<\/jats:p>","DOI":"10.1155\/2020\/2020161","type":"journal-article","created":{"date-parts":[[2020,6,1]],"date-time":"2020-06-01T23:30:47Z","timestamp":1591054247000},"page":"1-14","source":"Crossref","is-referenced-by-count":0,"title":["A New Numerical Approximation Method for Two-Dimensional Wave Equation with Neumann Damped Boundary"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8022-8317","authenticated-orcid":true,"given":"Jiankang","family":"Liu","sequence":"first","affiliation":[{"name":"Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, Shanxi, China"},{"name":"School of Mathematical Science, Shanxi University, Taiyuan 030006, Shanxi, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9243-7933","authenticated-orcid":true,"given":"Suying","family":"Zhang","sequence":"additional","affiliation":[{"name":"Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, Shanxi, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1137\/1030001"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1137\/0710073"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drs057"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/18.4.563"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1002\/num.21697"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(76)90110-8"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/s0893-9659(04)90019-5"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1137\/05063194x"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1137\/140973517"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1090\/s0025-5718-2014-02802-0"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(90)90165-i"},{"year":"1998","key":"13"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.11.002"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.05.010"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2017.09.013"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.04.027"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2007.07.018"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1002\/fld.2504"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1002\/fld.2652"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/428681"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1504\/pcfd.2015.070441"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2019.01.014"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1080\/00207160.2012.713475"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1080\/00207160.2012.754016"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1002\/1098-2426(200103)17:2<105::aid-num2>3.0.co;2-f"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1080\/01630563.2011.580874"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1002\/mma.534"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1081\/nfa-120022925"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1137\/0733026"},{"issue":"5","key":"31","doi-asserted-by":"crossref","first-page":"2623","DOI":"10.1016\/j.apm.2012.08.010","volume":"37","year":"2013","journal-title":"Applied Mathematical Modelling"},{"year":"2012","key":"32"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/2020161.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/2020161.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/2020161.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,1]],"date-time":"2020-06-01T23:30:50Z","timestamp":1591054250000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/2020161\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,1]]},"references-count":31,"alternative-id":["2020161","2020161"],"URL":"https:\/\/doi.org\/10.1155\/2020\/2020161","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2020,6,1]]}}}