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Therefore, this work presents a rational version of homotopy perturbation method (RHPM) as a novel tool with high potential to find approximate solutions for nonlinear differential equations. We present two case studies; for the first example, a comparison between the proposed method and the HPM method is presented; it will show how the RHPM generates highly accurate approximate solutions requiring less iteration, in comparison to results obtained by the HPM method. For the second example, which is a Van der Pol oscillator problem, we compare RHPM, HPM, and VIM, finding out that RHPM method generates the most accurate approximated solution.<\/jats:p>","DOI":"10.1155\/2012\/490342","type":"journal-article","created":{"date-parts":[[2012,9,20]],"date-time":"2012-09-20T21:02:13Z","timestamp":1348174933000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Rational Homotopy Perturbation Method"],"prefix":"10.1155","volume":"2012","author":[{"given":"H\u00e9ctor","family":"V\u00e1zquez-Leal","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,9,20]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.03.030"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2008.07.002"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-008-9248-9"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/124029"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/309123"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2003.08.008"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.06.003"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(99)00018-3"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(03)00341-2"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(01)00312-5"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-7462(98)00085-7"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.03.006"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2005.10.005"},{"key":"e_1_2_9_14_2","unstructured":"KhanY. 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