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We then explore the issue of optimal TVD Runge-Kutta methods for second, third and fourth order, and for low storage Runge-Kutta methods.<\/p>","DOI":"10.1090\/s0025-5718-98-00913-2","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"73-85","source":"Crossref","is-referenced-by-count":2060,"title":["Total variation diminishing Runge-Kutta schemes"],"prefix":"10.1090","volume":"67","author":[{"given":"Sigal","family":"Gottlieb","sequence":"first","affiliation":[]},{"given":"Chi-Wang","family":"Shu","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"key":"1","unstructured":"M. Carpenter and C. 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