{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T20:35:36Z","timestamp":1790282136911,"version":"4.1.0"},"reference-count":38,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this research study, a bilinear Chebyshev pseudo-spectral method is considered to solve the two-dimensional nonlinear acoustic wave equation and extended to solve the three-dimensional nonlinear wave equations. First, the wave equation is spatially approximated by a bilinear Chebyshev pseudo-spectral method and a second-order Sylvester-type matrix differential equation (MDE) is obtained. Using an eigenvalue decomposition method, this equation is transformed to a set of separated second-order ODEs in the new coordinates. Finally, using an implicit Runge\u2013Kutta\u2013Nystr\u00f6m (IRKN) or stabilized Numerov method, the arising second-order ODEs will be solved. Transforming into a set of separated second-order ODEs causes one to reduce the computational complexity. Specifically, in the higher dimensional models, the cost of computation is considerably reduced. The convergence analysis is also investigated theoretically. Furthermore, the conservation of energy is numerically investigated. Finally, Some numerical examples are included to confirm the accuracy and efficiency and the fast computing behavior of the approach. These examples represent that our approach has superiority over the Kronecker approach.<\/jats:p>","DOI":"10.1137\/22m1506390","type":"journal-article","created":{"date-parts":[[2023,7,5]],"date-time":"2023-07-05T04:39:26Z","timestamp":1688531966000},"page":"B413-B439","source":"Crossref","is-referenced-by-count":5,"title":["Fast Computing Approaches Based on a Bilinear Pseudo-Spectral Method for Nonlinear Acoustic Wave Equations"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2581-0662","authenticated-orcid":true,"given":"Manoochehr","family":"Khasi","sequence":"first","affiliation":[{"name":"School of Mathematics, Iran University of Science and Technology, Tehran 13114-16846, Iran."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9177-900X","authenticated-orcid":true,"given":"Jalil","family":"Rashidinia","sequence":"additional","affiliation":[{"name":"School of Mathematics, Iran University of Science and Technology, Tehran 13114-16846, Iran."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8420-5414","authenticated-orcid":true,"given":"Mohammad Navaz","family":"Rasoulizadeh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Basic Sciences, Velayat University, Iranshar 99111-31311, Iran."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,7,5]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.06.029"},{"key":"ref2","volume-title":"Elementary Differential Equations and Boundary Value Problems","author":"Boyce W. 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