Recasting nonlinear differential equations as S-systems: a canonical nonlinear form
dc.contributor.author | Savageau, Michael A. | en_US |
dc.contributor.author | Voit, Eberhard O. | en_US |
dc.date.accessioned | 2006-04-07T19:46:13Z | |
dc.date.available | 2006-04-07T19:46:13Z | |
dc.date.issued | 1987-11 | en_US |
dc.identifier.citation | Savageau, Michael A., Voit, Eberhard O. (1987/11)."Recasting nonlinear differential equations as S-systems: a canonical nonlinear form." Mathematical Biosciences 87(1): 83-115. <http://hdl.handle.net/2027.42/26514> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6VHX-45F5T8F-18/2/1836e872596eab1cb341c8238c23e117 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/26514 | |
dc.description.abstract | An enormous variety of nonlinear differential equations and functions have been recast exactly in the canonical form called an S-system. This is a system of nonlinear ordinary differential equations, each with the same structure: the change in a variable is equal to a difference of products of power-law functions. We review the development of S-systems, prove that the minimum for the range of equations that can be recast as S-systems consists of all equations composed of elementary functions and nested elementary functions of elementary functions, give a detailed example of the recasting process, and discuss the theoretical and practical implications. Among the latter is the ability to solve numerically nonlinear ordinary differential equations in their S-system form significantly faster than in their original form through utilization of a specially designed algorithm. | en_US |
dc.format.extent | 1795766 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | Recasting nonlinear differential equations as S-systems: a canonical nonlinear form | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Public Health | en_US |
dc.subject.hlbsecondlevel | Statistics and Numeric Data | en_US |
dc.subject.hlbsecondlevel | Natural Resources and Environment | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbsecondlevel | Ecology and Evolutionary Biology | en_US |
dc.subject.hlbsecondlevel | Biological Chemistry | en_US |
dc.subject.hlbtoplevel | Social Sciences | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.subject.hlbtoplevel | Health Sciences | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Microbiology and Immunology, The University of Michigan, Ann Arbor, Michigan 48109 USA | en_US |
dc.contributor.affiliationum | Department of Microbiology and Immunology, The University of Michigan, Ann Arbor, Michigan 48109 USA | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/26514/1/0000052.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0025-5564(87)90035-6 | en_US |
dc.identifier.source | Mathematical Biosciences | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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