{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T10:23:28Z","timestamp":1789727008103,"version":"4.0.1"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["633724"],"award-info":[{"award-number":["633724"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42274101"],"award-info":[{"award-number":["42274101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41874086"],"award-info":[{"award-number":["41874086"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009993","name":"Excellent Youth Foundation of Heilongjiang Province of China","doi-asserted-by":"publisher","award":["2018JJ1042"],"award-info":[{"award-number":["2018JJ1042"]}],"id":[{"id":"10.13039\/501100009993","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,4,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper new innovative fourth order compact schemes for Robin and Neumann boundary conditions have been developed for boundary value problems of elliptic PDEs in two and three dimensions. Different from the traditional finite difference operator approach, which may not work for the flux type of boundary conditions, carefully designed undetermined coefficient methods are utilized in developing high order compact (HOC) schemes. The new methods not only can be utilized to design HOC schemes for flux type boundary conditions but also can be applied to general elliptic PDEs including Poisson, Helmholtz, diffusion-advection, and anisotropic equations with linear boundary conditions. In the newly developed HOC methods, the coefficient matrices are generally M-matrices, which guarantee the discrete maximum principle for well-posed problems, so the convergence of the HOC methods. The developed HOC methods are versatile and can cover most HOC schemes in the literature. The HOC methods for Robin boundary conditions and for anisotropic diffusion and advection equations with Robin or even Dirichlet boundary conditions are likely the first ones that have ever been developed. With the help of pseudoinverse or singular value decomposition, we have also observed that the developed HOC methods usually have smaller error constants compared with traditional HOC methods when applicable. Nontrivial examples with large wave numbers and oscillatory solutions are presented to confirm the performance of the new HOC methods.<\/jats:p>","DOI":"10.1137\/21m1444771","type":"journal-article","created":{"date-parts":[[2023,4,12]],"date-time":"2023-04-12T06:09:19Z","timestamp":1681279759000},"page":"A646-A674","source":"Crossref","is-referenced-by-count":15,"title":["High Order Compact Schemes for Flux Type BCs"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1636-5376","authenticated-orcid":true,"given":"Zhilin","family":"Li","sequence":"first","affiliation":[{"name":"CRSC and Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5768-7972","authenticated-orcid":true,"given":"Kejia","family":"Pan","sequence":"additional","affiliation":[{"name":"Corresponding author. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha 410083, Hunan, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,4,26]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/050622833"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/0902022"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1002\/fld.4791"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1002\/num.20476"},{"key":"ref5","first-page":"98","volume":"26","author":"Fu Y.","year":"2008","journal-title":"J. Comput. Math."},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2015.05.027"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.5627"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4288-8"},{"key":"ref9","first-page":"29","volume":"15","author":"Il\u2019in V. P.","year":"2000","journal-title":"Russian J. Numer. 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