Identification of the initial function for nonlinear delay differential equations
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C. T. H. Baker
We consider a 'data assimilation problem' for nonlinear delay differential equations. Our problem is to find an initial function that gives rise to a solution of a given nonlinear delay differential equation, which is a close fit to observed data. A role for adjoint equations and fundamental solutions in the nonlinear case is established. A 'pseudo-Newton' method is presented. Our results extend those given by the authors in [(C. T. H. Baker and E. I. Parmuzin, Identification of the initial function for delay differential equation: Part I: The continuous problem & an integral equation analysis. NA Report No. 431, MCCM, Manchester, England, 2004.), (C. T. H. Baker and E. I. Parmuzin, Analysis via integral equations of an identification problem for delay differential equations. J. Int. Equations Appl. (2004) 16, 111–135.)] for the case of linear delay differential equations.
Copyright 2005, Walter de Gruyter
Articles in the same Issue
- Inverse problems of the mathematical theory of tides: boundary-function problem
- Study and solution of identification problems for nonstationary 2D and 3D convection–diffusion equations
- Identification of the initial function for nonlinear delay differential equations
- Solvability of a tide dynamics model in adjacent seas
- Variational data assimilation for a nonstationary heat conduction problem with nonlinear diffusion
- Mathematical model of sea dynamics in a σ-coordinate system
Articles in the same Issue
- Inverse problems of the mathematical theory of tides: boundary-function problem
- Study and solution of identification problems for nonstationary 2D and 3D convection–diffusion equations
- Identification of the initial function for nonlinear delay differential equations
- Solvability of a tide dynamics model in adjacent seas
- Variational data assimilation for a nonstationary heat conduction problem with nonlinear diffusion
- Mathematical model of sea dynamics in a σ-coordinate system
