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In present method, the required weighting coefficients are computed using modified quartic Hyperbolic B-spline as a basis function. These coupled 1D and coupled 2D Burgers' equations got transformed into the set of ordinary differential equations, tackled by SSPRK43 scheme. Efficiency of the scheme and exactness of the obtained numerical solutions is declared with the aid of 8 numerical examples. Numerical results obtained by modified quartic Hyperbolic B-spline are efficient and it is easy to implement</jats:p></jats:abstract><publication_date media_type="online"><month>4</month><day>7</day><year>2021</year></publication_date><publication_date media_type="print"><month>4</month><day>7</day><year>2021</year></publication_date><pages><first_page>37</first_page><last_page>55</last_page></pages><ai:program xmlns:ai="http://www.crossref.org/AccessIndicators.xsd" name="AccessIndicators"><ai:free_to_read start_date="2021-04-07"/><ai:license_ref applies_to="am" start_date="2021-04-07">https://www.naun.org/main/NAUN/mechanics/2021/a102003-005(2021).pdf</ai:license_ref></ai:program><archive_locations><archive name="Portico"/></archive_locations><doi_data><doi>10.46300/9104.2021.15.5</doi><resource>https://www.naun.org/main/NAUN/mechanics/2021/a102003-005(2021).pdf</resource></doi_data><citation_list><citation key="ref0"><doi>10.1103/physreve.52.3711</doi><unstructured_citation>S. E. 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