Stability properties of interpolants for Runge-Kutta methods
SIAM Journal on Numerical Analysis
Effective solution of discontinuous IVPs using a Runge-Kutta formula pair with interpolants
Applied Mathematics and Computation
SIAM Journal on Applied Mathematics
The tracking of derivative discontinuities in systems of delay-differential equations
Selected papers from the international conference on Numerical solution of Volterra and delay equations
Developing a delay differential equation solver
Selected papers from the international conference on Numerical solution of Volterra and delay equations
The adaptation of STRIDE to delay differential equations
Selected papers from the international conference on Numerical solution of Volterra and delay equations
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Applied Numerical Mathematics - Special issue to honor professor J. C. Butcher on his sixtieth birthday
Pitfalls in Parameter Estimation for Delay Differential Equations
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Automatic Integration of Functional Differential Equations: An Approach
ACM Transactions on Mathematical Software (TOMS)
Designing efficient software for solving delay differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Ordinary Differential Equations
Ordinary Differential Equations
Sensitivity analysis for dynamic systems with time-lags
Journal of Computational and Applied Mathematics
Solving ODEs and DDEs with residual control
Applied Numerical Mathematics
Rival approaches to mathematical modelling in immunology
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Open issues in devising software for the numerical solution of implicit delay differential equations
Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
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This article deals with initial value problem solutions in systems of delay differential equations and their derivatives with respect to parameters, where the parameters may occur in the initial value, the initial function, the right-hand-side function, and the delay. Sufficient conditions for differentiability are given, and an efficient and reliable method for the numerical computation is presented. Emphasis is laid on the treatment of problems with a discontinuity at the initial time, for which it is shown that jumps occur in the derivative at the propagated discontinuity times. An explicit expression for the size of the jumps in the derivative is given. Features are discussed of the implementation of COLSOL-DDE, an experimental solver for initial value problems in delay differential equations that also computes the derivatives of the solution. The performance of the developed method is demonstrated by a comparison to standard techniques for derivative approximation.