{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:48Z","timestamp":1740134568943,"version":"3.37.3"},"reference-count":43,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41230420","2012CB417404","11-1-4-95-jch"],"award-info":[{"award-number":["41230420","2012CB417404","11-1-4-95-jch"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Basic Research Program of China","doi-asserted-by":"crossref","award":["41230420","2012CB417404","11-1-4-95-jch"],"award-info":[{"award-number":["41230420","2012CB417404","11-1-4-95-jch"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Basic Research Program of Qingdao Science and Technology Plan","award":["41230420","2012CB417404","11-1-4-95-jch"],"award-info":[{"award-number":["41230420","2012CB417404","11-1-4-95-jch"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>A 1.5-layer reduced-gravity shallow-water ocean model in spherical coordinates is described and discretized in a staggered grid (standard Arakawa C-grid) with the forward-time central-space (FTCS) method and the Leap-frog finite difference scheme. The discrete Fourier analysis method combined with the Gershgorin circle theorem is used to study the stability of these two finite difference numerical models. A series of necessary conditions of selection criteria for the time-space step sizes and model parameters are obtained. It is showed that these stability conditions are more accurate than the Courant-Friedrichs-Lewy (CFL) condition and other two criterions (Blumberg and Mellor, 1987; Casulli, 1990, 1992). Numerical experiments are proposed to test our stability results, and numerical model that is designed is also used to simulate the ocean current.<\/jats:p>","DOI":"10.1155\/2013\/478054","type":"journal-article","created":{"date-parts":[[2013,11,6]],"date-time":"2013-11-06T21:07:50Z","timestamp":1383772070000},"page":"1-12","source":"Crossref","is-referenced-by-count":1,"title":["Stability Analysis of Numerical Methods for a 1.5-Layer Shallow-Water Ocean Model"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2350-2030","authenticated-orcid":true,"given":"Guang-an","family":"Zou","sequence":"first","affiliation":[{"name":"Key Laboratory of Ocean Circulation and Wave, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, 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