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Article

Chleboun, Jan ; Mikeš, Karel
Identification of parameters in initial value problems for ordinary differential equations. (English). In: Chleboun, J., Přikryl, P., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 8-13, 2014. Institute of Mathematics AS CR, Prague, 2015. pp. 58-63
MSC: 49K40, 65L05
Keywords:
computer algebra; gradient algorithm
Summary:
Scalar parameter values as well as initial condition values are to be identified in initial value problems for ordinary differential equations (ODE). To achieve this goal, computer algebra tools are combined with numerical tools in the MATLAB environment. The best fit is obtained through the minimization of the summed squares of the difference between measured data and ODE solution. The minimization is based on a gradient algorithm where the gradient of the summed squares is calculated either numerically or via auxiliary initial value problems. In the latter case, the MATLABR Symbolic Math Toolbox is used to derive the expressions that define the auxiliary problems and to transform them into MATLAB routines.
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