ACM Transactions on Mathematical Software (TOMS)
Journal of Computational and Applied Mathematics - Special issue on SQP-based direct discretization methods for practical optimal control problems
Numerical modelling in biosciences using delay differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Retarded differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Four-dimensional variational data assimilation for Doppler radar wind data
Journal of Computational and Applied Mathematics
Sense from sensitivity and variation of parameters
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Sense from sensitivity and variation of parameters
Applied Numerical Mathematics
Four-dimensional variational data assimilation for Doppler radar wind data
Journal of Computational and Applied Mathematics
Original article: Numerical computation of derivatives in systems of delay differential equations
Mathematics and Computers in Simulation
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Many problems in bioscience for which observations are reported in the literature can be modelled by suitable functional differential equations incorporating time-lags (other terminology: delays) or memory effects, parameterized by scientifically meaningful constant parameters p or/and variable parameters (for example, control functions) u(t). It is often desirable to have information about the effect on the solution of the dynamic system of perturbing the initial data, control functions, time-lags and other parameters appearing in the model. The main purpose of this paper is to derive a general theory for sensitivity analysis of mathematical models that contain time-lags. In this paper, we use adjoint equations and direct methods to estimate the sensitivity functions when the parameters appearing in the model are not only constants but also variables of time. To illustrate the results, the methodology is applied numerically to an example of a delay differential model.