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A monotone piecewise cubic interpolation is used in the central schemes to give an accurate approximation for the model in question. The monotonicity parameter introduced in part I is found to be important. That parameter, along with the Courant\u2013Friedrichs\u2013Lewy (CFL) number, plays a major role in the criteria for monotonicity and stability of the central schemes. The modified scheme is tested on several conservation laws taking a CFL number equal or close to unity, and the scheme is found to be accurate and robust.<\/jats:p>","DOI":"10.1137\/100784473","type":"journal-article","created":{"date-parts":[[2010,9,7]],"date-time":"2010-09-07T18:10:25Z","timestamp":1283883025000},"page":"2793-2819","source":"Crossref","is-referenced-by-count":2,"title":["On Stability, Monotonicity, and Construction of Difference Schemes II: Applications"],"prefix":"10.1137","volume":"32","author":[{"given":"V. 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