{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T07:22:08Z","timestamp":1777101728942,"version":"3.51.4"},"reference-count":10,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,10,10]],"date-time":"2020-10-10T00:00:00Z","timestamp":1602288000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007345","name":"King Mongkut's University of Technology North Bangkok","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007345","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2020,10,10]]},"abstract":"<jats:p>Analyzing and improving mathematical models for water quality investigation are imperative for water quality issues around the world. This study is aimed at presenting the 1D unsteady state regarding analytical and numerical solutions of dissolved oxygen (DO) concentration in a river, in which the increase of pollution from a source is considered as an exponential term. Laplace transformation was utilized to obtain analytical solutions, while the finite difference technique was selected for numerical solutions. The results show that the rate of pollutant addition along the river (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>q<\/mml:mi><\/mml:math>) and the arbitrary constants of an exponentially increasing pollution source term (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>\u03bb<\/mml:mi><\/mml:math>) affected inversely, while the initial concentration <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:msub><mml:mrow><mml:mi>X<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>i<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:math> affected directly, DO in the river. These solutions and simulations can be enabled for testing in various scenarios in terms of the behavior of oxygen depletion in polluted rivers.<\/jats:p>","DOI":"10.1155\/2020\/9085981","type":"journal-article","created":{"date-parts":[[2020,10,11]],"date-time":"2020-10-11T02:35:19Z","timestamp":1602383719000},"page":"1-7","source":"Crossref","is-referenced-by-count":12,"title":["Water Quality Analysis for the Depletion of Dissolved Oxygen due to Exponentially Increasing Form of Pollution Sources"],"prefix":"10.1155","volume":"2020","author":[{"given":"N.","family":"Manitcharoen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Mongkut\u2019s Institute of Technology Ladkrabang, Bangkok 10520, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2550-7484","authenticated-orcid":true,"given":"B.","family":"Pimpunchat","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Mongkut\u2019s Institute of Technology Ladkrabang, Bangkok 10520, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Sattayatham","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Mongkut\u2019s Institute of Technology Ladkrabang, Bangkok 10520, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"3","volume-title":"The effects of dissolved oxygen on fish growth in aquaculture","year":"2007"},{"key":"4","year":"2007"},{"key":"6","year":"1925"},{"key":"7","year":"1997"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jhydrol.2009.11.008"},{"key":"9","first-page":"2431","volume-title":"Modelling river pollution and removal by aeration","year":"2007"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2008.03.026"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/9504835"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.20852\/ntmsci.2017.184"},{"key":"13","year":"1969"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2020\/9085981.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2020\/9085981.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2020\/9085981.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,11]],"date-time":"2020-10-11T12:58:37Z","timestamp":1602421117000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/jam\/2020\/9085981\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,10]]},"references-count":10,"alternative-id":["9085981","9085981"],"URL":"https:\/\/doi.org\/10.1155\/2020\/9085981","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,10]]}}}