Childs, S. Bart; Osborne, Michael R. Fitting solutions of ordinary differential equations to observed data. (English) Zbl 0909.65040 May, Robert L. (ed.) et al., Computational techniques and applications: CTAC 95. Proceedings of the 7th biennial conference, Swinburne Univ. of Technology, Melbourne, Australia, July 3–5 1995. Singapore: World Scientific. 193-198 (1996). In this paper, the asymptotic stability and asymptotic rates of convergence for large \(n\) are considered for the parameter estimation problem. The use of Fisher’s method of scoring is summarized. Here this is equivalent to the Gauss-Newton algorithm. The excellent numerical properties of the scoring algorithm are stressed. These are exemplified in the final section where it is applied to a system for modelling the spring mass dashpot. Numerical results obtained usig the code ps\(_-\)quasi are reported.For the entire collection see [Zbl 0897.00034]. Cited in 1 Document MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 34A55 Inverse problems involving ordinary differential equations Keywords:inverse problems; numerical results; asymptotic stability; convergence; parameter estimation; Fisher’s method of scoring; Gauss-Newton algorithm; spring mass dashpot PDFBibTeX XMLCite \textit{S. B. Childs} and \textit{M. R. Osborne}, in: Computational techniques and applications: CTAC 95. Proceedings of the 7th biennial conference, Swinburne Univ. of Technology, Melbourne, Australia, July 3--5 1995. Singapore: World Scientific. 193--198 (1996; Zbl 0909.65040)