{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T13:11:36Z","timestamp":1779369096522,"version":"3.53.0"},"reference-count":64,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,9,30]],"date-time":"2023-09-30T00:00:00Z","timestamp":1696032000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>In this paper, we introduce a novel approach employing two-dimensional uniform and non-uniform Haar wavelet collocation methods to effectively solve the generalized Burgers\u2013Huxley and Burgers\u2013Fisher equations. The demonstrated method exhibits an impressive quartic convergence rate. Several test problems are presented to exemplify the accuracy and efficiency of this proposed approach. Our results exhibit exceptional accuracy even with a minimal number of spatial divisions. Additionally, we conduct a comparative analysis of our results with existing methods.<\/jats:p>","DOI":"10.3390\/computation11100189","type":"journal-article","created":{"date-parts":[[2023,10,1]],"date-time":"2023-10-01T16:58:09Z","timestamp":1696179489000},"page":"189","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Two-Dimensional Uniform and Non-Uniform Haar Wavelet Collocation Approach for a Class of Nonlinear PDEs"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0647-6600","authenticated-orcid":false,"given":"Narendra","family":"Kumar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Jodhpur, Jodhpur 342030, Rajasthan, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8768-094X","authenticated-orcid":false,"given":"Amit K.","family":"Verma","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Patna, Bihta, Patna 801106, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0634-2370","authenticated-orcid":false,"given":"Ravi P.","family":"Agarwal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Texas A & M University-Kingsville, 700 University Blvd., MSC 172, Kingsville, TX 78363-8202, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1016\/j.nonrwa.2007.10.014","article-title":"The Homotopy analysis method to solve the Burgers-Huxley Equation","volume":"10","author":"Molabahrami","year":"2009","journal-title":"Nonlinear Anal. 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