{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T12:09:59Z","timestamp":1759838999625,"version":"3.41.0"},"reference-count":12,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[1986,12,1]],"date-time":"1986-12-01T00:00:00Z","timestamp":533779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[1986,12]]},"abstract":"<jats:p>Solving flame propagation problems with the method of lines leads to large systems of ordinary differential equations. These systems are usually solved by Backward Differentiation Formula (BDF) methods, such as by LSODE of Hindmarsh. Recently, Rosenbrock methods turned out to be rather successful for integrating small systems with inexpensive function and Jacobian evaluations. However, no test has been done on the performance of some recently developed Rosenbrock codes in a situation in which the dimension of the system is large, for example, over one hundred equations. These Rosenbrock codes performed quite well on the STIFF DETEST and other small systems. The aim of this paper is to investigate the performance of the Rosenbrock methods in solving the flame propagation problem by the method of lines.<\/jats:p>","DOI":"10.1145\/22721.22722","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:29:03Z","timestamp":1027769343000},"page":"354-361","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["The solution of a combustion problem with Rosenbrock methods"],"prefix":"10.1145","volume":"12","author":[{"given":"A.","family":"Ostermann","sequence":"first","affiliation":[{"name":"Univ. Innsbruck, Innsbruck, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Kaps","sequence":"additional","affiliation":[{"name":"Univ. Innsbruck, Innsbruck, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T. 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Institutsnotiz 3 , Institut for Mathematik und Geometrie, Technikerst. 13, A-6020 Innsbruck, Austria .]] KAPS, P., AND OSTERMANN, A. Rosenbrock methods using few LU-decompositions. Institutsnotiz 3, Institut for Mathematik und Geometrie, Technikerst. 13, A-6020 Innsbruck, Austria.]]"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/BF02242171","article-title":"Rosenbrock methods for stiff ODEs: A comparison of Richardson extrapolation and embedding technique","volume":"34","author":"KAPS P.","year":"1985","unstructured":"KAPS , P. , POON , S. W. H., AND BuI , T.D . Rosenbrock methods for stiff ODEs: A comparison of Richardson extrapolation and embedding technique . Computing 34 ( 1985 ), 17 - 40 .]] KAPS, P., POON, S. W. H., AND BuI, T.D. Rosenbrock methods for stiff ODEs: A comparison of Richardson extrapolation and embedding technique. Computing 34 (1985), 17-40.]]","journal-title":"Computing"},{"key":"e_1_2_1_8_2","first-page":"55","article-title":"Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differen~Lial equations","volume":"33","author":"KAPS P.","year":"1979","unstructured":"KAPS , P. , AND RENTROP , P . Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differen~Lial equations . Nurner. Math. 33 ( 1979 ), 55 - 68 .]] KAPS, P., AND RENTROP, P. Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differen~Lial equations. Nurner. Math. 33 (1979), 55-68.]]","journal-title":"Nurner. Math."},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","first-page":"606","DOI":"10.2514\/3.61184","article-title":"Numerical study of the interaction of fast chemistry and diffusion","volume":"17","author":"OTEY G. R.","year":"1979","unstructured":"OTEY , G. R. , AND DWYER , H.A . Numerical study of the interaction of fast chemistry and diffusion . Am. Inst. Aeronaut. Astronaut. J. 17 ( 1979 ), 606 - 613 .]] OTEY, G. R., AND DWYER, H.A. Numerical study of the interaction of fast chemistry and diffusion. Am. Inst. Aeronaut. Astronaut. J. 17 (1979), 606-613.]]","journal-title":"Am. Inst. Aeronaut. Astronaut. J."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1145\/355993.355994"},{"key":"e_1_2_1_11_2","first-page":"45","volume":"18","author":"VAN VELDHUIZEN M","year":"1981","unstructured":"VAN VELDHUIZEN , M . D-stability. Siam J. Nurner. Anal. 18 ( 1981 ), 45 - 64 .]] VAN VELDHUIZEN, M. D-stability. Siam J. Nurner. Anal. 18 (1981), 45-64.]]","journal-title":"D-stability. Siam J. Nurner. 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