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The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three\u2010level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have been compared with the exact solutions reported in previous studies. The <jats:italic>L<\/jats:italic><jats:sub>2<\/jats:sub>,\u2009<jats:italic>L<\/jats:italic><jats:sub><jats:italic>\u221e<\/jats:italic><\/jats:sub> and Root\u2010Mean\u2010Square (RMS) errors in the solutions show that the scheme is accurate and effective.<\/jats:p>","DOI":"10.1155\/2012\/925920","type":"journal-article","created":{"date-parts":[[2012,6,5]],"date-time":"2012-06-05T15:27:30Z","timestamp":1338910050000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Multilevel Finite Difference Scheme for One\u2010Dimensional Burgers Equation Derived from the Lattice Boltzmann Method"],"prefix":"10.1155","volume":"2012","author":[{"given":"Qiaojie","family":"Li","sequence":"first","affiliation":[]},{"given":"Zhoushun","family":"Zheng","sequence":"additional","affiliation":[]},{"given":"Shuang","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Jiankang","family":"Liu","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,5,29]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.56.1505"},{"key":"e_1_2_7_2_2","series-title":"Annual Review of Fluid Mechanics","first-page":"329","volume-title":"Annual Review of Fluid Mechanics","author":"Chen S.","year":"1998"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0370-1573(92)90090-M"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1085048"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.61.2332"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.56.6811"},{"key":"e_1_2_7_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2009.05.047"},{"key":"e_1_2_7_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2007.06.033"},{"key":"e_1_2_7_9_2","doi-asserted-by":"publisher","DOI":"10.1299\/jsmeb.44.45"},{"key":"e_1_2_7_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-08276-8"},{"key":"e_1_2_7_11_2","first-page":"172","article-title":"Lattice Boltzmann method for Burgers equation","volume":"17","author":"Shen Z. 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