Rootfinding and interpolation with Runge-Kutta-Sarafyan methods
Transactions of the Society for Computer Simulation International
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Journal of Computational and 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
DELSOL: a numerical code for the solution of systems of delay-differential equations
Selected papers from the international conference on Numerical solution of Volterra and delay 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
Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
Automatic Integration of Functional Differential Equations: An Approach
ACM Transactions on Mathematical Software (TOMS)
Algorithm 497: Automatic Integration of Functional Differential Equations [D2]
ACM Transactions on Mathematical Software (TOMS)
Control of Interpolatory Error in Retarded Differential Equations
ACM Transactions on Mathematical Software (TOMS)
Solving ODEs and DDEs with residual control
Applied Numerical Mathematics
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
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This manuscript presents many detailed studies of the numerical solution (by the restart method) of a general class of functional differential equations with state dependent lags; that is, where the delays depend upon the (unknown) solution. It emphasizes the sharpness of earlier published results, including those that relate the multiplicity of various shifted zeros of the lag function to the rates of convergence of methods for locating these zeros and to the rates of convergence of the global solution of the delay equation. The studies were selected to clarify the unusual aspects of numerical methods for delay equations, particularly those with state dependent lags. Although the results given here are mainly analytical in nature, they are ones that every numerical analyst and software designer interested in delay equations should master since they form the technological basis for modern software for state dependent delay differential equations. Indeed, almost all modern delay equation software, in one form or another, is based on these results.