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This work presents the rational biparameter homotopy perturbation method (RBHPM) as a novel tool with the potential to find approximate solutions for nonlinear differential equations. The method generates the solutions in the form of a quotient of two power series of different homotopy parameters. Besides, in order to improve accuracy, we propose the Laplace\u2010Pad\u00e9 rational biparameter homotopy perturbation method (LPRBHPM), when the solution is expressed as the quotient of two truncated power series. The usage of the method is illustrated with two case studies. On one side, a Ricatti nonlinear differential equation is solved and a comparison with the homotopy perturbation method (HPM) is presented. On the other side, a nonforced Van der Pol Oscillator is analysed and we compare results obtained with RBHPM, LPRBHPM, and HPM in order to conclude that the LPRBHPM and RBHPM methods generate the most accurate approximated solutions.<\/jats:p>","DOI":"10.1155\/2012\/923975","type":"journal-article","created":{"date-parts":[[2012,12,2]],"date-time":"2012-12-02T21:17:34Z","timestamp":1354483054000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Rational Biparameter Homotopy Perturbation Method and Laplace\u2010Pad\u00e9 Coupled Version"],"prefix":"10.1155","volume":"2012","author":[{"given":"Hector","family":"Vazquez-Leal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arturo","family":"Sarmiento-Reyes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yasir","family":"Khan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Uriel","family":"Filobello-Nino","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alejandro","family":"Diaz-Sanchez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2012,12,2]]},"reference":[{"key":"e_1_2_11_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.03.030"},{"key":"e_1_2_11_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2008.07.002"},{"key":"e_1_2_11_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2010.05.006"},{"key":"e_1_2_11_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2008.07.060"},{"key":"e_1_2_11_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2007.04.072"},{"key":"e_1_2_11_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.04.013"},{"key":"e_1_2_11_7_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/490342"},{"key":"e_1_2_11_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-008-9248-9"},{"key":"e_1_2_11_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2003.08.008"},{"key":"e_1_2_11_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.06.003"},{"key":"e_1_2_11_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(99)00018-3"},{"key":"e_1_2_11_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(03)00341-2"},{"key":"e_1_2_11_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(01)00312-5"},{"key":"e_1_2_11_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-7462(98)00085-7"},{"key":"e_1_2_11_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.03.006"},{"key":"e_1_2_11_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2005.10.005"},{"key":"e_1_2_11_17_2","unstructured":"KhanY. 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