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
The numerical solution of delay-differential-algebraic equations of retarded and neutral type
SIAM Journal on Numerical Analysis
Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
SIAM Journal on Numerical Analysis
Automatic Integration of Functional Differential Equations: An Approach
ACM Transactions on Mathematical Software (TOMS)
Retarded differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Numerical Solution of Implicit Neutral Functional Differential Equations
SIAM Journal on Numerical Analysis
Differential algebraic equations with after-effect
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Computational approaches to parameter estimation and model selection in immunology
Journal of Computational and Applied Mathematics - Special issue: Mathematics applied to immunology
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
Journal of Computational and Applied Mathematics
Computational approaches to parameter estimation and model selection in immunology
Journal of Computational and Applied Mathematics - Special issue: Mathematics applied to immunology
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It is well known that the solutions of delay differential and implicit and explicit neutral delay differential equations (NDDEs) may have discontinuous derivatives, but it has not been appreciated (sufficiently) that the solutions of NDDEs-and, therefore, solutions of delay differential algebraic equations-need not be continuous. Numerical codes for solving differential equations, with or without retarded arguments, are generally based on the assumption that a solution is continuous. We illustrate and explain how the discontinuities arise, and present some methods to deal with these problems computationally. The investigation of a simple example is followed by a discussion of more general NDDEs and further mathematical detail.