{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:35:55Z","timestamp":1760060155200,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,1]],"date-time":"2025-08-01T00:00:00Z","timestamp":1754006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Henan Provincial Natural Science Foundation","award":["242300421392","252102220057"],"award-info":[{"award-number":["242300421392","252102220057"]}]},{"name":"The Science and Technology Key Project of Henan Province of China","award":["242300421392","252102220057"],"award-info":[{"award-number":["242300421392","252102220057"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>In this paper, we propose the MUSWENO scheme, a novel mapped weighted essentially non-oscillatory (WENO) method that employs unequal-sized stencils, for solving nonlinear degenerate parabolic equations. The new mapping function and nonlinear weights are proposed to reduce the difference between the linear weights and nonlinear weights. Smaller numerical errors and fifth-order accuracy are obtained. Compared with traditional WENO schemes, this new scheme offers the advantage that linear weights can be any positive numbers on the condition that their summation is one, eliminating the need to handle cases with negative linear weights. Another advantage is that we can reconstruct a polynomial over the large stencil, while many classical high-order WENO reconstructions only reconstruct the values at the boundary points or discrete quadrature points. Extensive examples have verified the good representations of this scheme.<\/jats:p>","DOI":"10.3390\/computation13080182","type":"journal-article","created":{"date-parts":[[2025,8,4]],"date-time":"2025-08-04T09:41:17Z","timestamp":1754300477000},"page":"182","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A New Type of High-Order Mapped Unequal-Sized WENO Scheme for Nonlinear Degenerate Parabolic Equations"],"prefix":"10.3390","volume":"13","author":[{"given":"Zhengwei","family":"Hou","sequence":"first","affiliation":[{"name":"School of Mining Engineering, Heilongjiang University of Science and Technology, Harbin 150022, China"}]},{"given":"Liang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Huang Huai University, Zhumadian 463000, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,1]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Aronson, D.G. 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