Practical aspects of interpolation in Runge-Kutta codes
SIAM Journal on Scientific and Statistical Computing
Robust defect control with Runge-Kutta schemes
SIAM Journal on Numerical Analysis
Runge-Kutta defect control using Hermite-Birkhoff interpolation
SIAM Journal on Scientific and Statistical Computing
Runge-Kutta Software with Defect Control four Boundary Value ODEs
SIAM Journal on Scientific Computing
Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
The evaluation of numerical software for delay differential equations
Proceedings of the IFIP TC2/WG2.5 working conference on Quality of numerical software: assessment and enhancement
A BVP solver based on residual control and the Maltab PSE
ACM Transactions on Mathematical Software (TOMS)
Solving ODEs with MATLAB
Sharpness results for state dependent delay differential equations: an overview
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Delay-differential-algebraic equations in control theory
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Journal of Computational and Applied Mathematics
Sharpness results for state dependent delay differential equations: An overview
Applied Numerical Mathematics
Applied Numerical Mathematics
Delay-differential-algebraic equations in control theory
Applied Numerical Mathematics
SIAM Journal on Scientific Computing
Original article: Numerical computation of derivatives in systems of delay differential equations
Mathematics and Computers in Simulation
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We first consider the numerical integration of ordinary differential equations (ODEs) with Runge-Kutta methods that have continuous extensions. For some methods of this kind we develop robust and inexpensive estimates of both the local error and the size of the residual. We then develop an effective program, ddesd, to solve delay differential equations (DDEs) with time- and state-dependent delays. To get reliable results for these difficult problems, the code estimates and controls the size of the residual. The user interface of ddesd makes it easy to formulate and solve DDEs, even those with complications like event location and restarts.