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A numerical experiment on the determination of unknown parameters in an analytic system of ordinary differential equations

Authors
Journal
Mathematical Biosciences
0025-5564
Publisher
Elsevier
Publication Date
Volume
3
Identifiers
DOI: 10.1016/0025-5564(68)90084-9
Disciplines
  • Mathematics

Abstract

Abstract For the reaction A+B ⇄ k −1=0.5 k 1=0.5 C , the concentration C = C( t), 0 ⩽ t ⩽ 2 is computed for two cases of initial data A 0, B 0, C 0 from the usual system of ordinary differential equations. The results ( k 1, k −1) of fitting the data C = C( t), 0 ⩽ t ⩽ 2, using the method of least squares via Newton's method for solving nonlinear systems of equations, are discussed. With only roundoff error in the data, the theoretical constants k 1 = 0.5 and k −1 = 0.5 are obtained from the least squares process. The effect of various errors in the data A 0, B 0, C 0, and C = C( t), 0 ⩽ t ⩽ 2, on the computed ( k 1, k -1) is presented and discussed.

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