A delay differential equation solver based on a continuous Runge-Kutta method with defect control. (English) Zbl 1005.65071
Summary: We have recently developed a generic approach for solving neutral delay differential equations based on the use of a continuous Runge-Kutta formula with defect control and investigated its convergence properties. In this paper, we describe a method, DDVERK, which implements this approach and justify the strategies and heuristics that have been adopted. In particular we show how the assumptions related to error control, stepsize control, and discontinuity detection (required for convergence) can be efficiently realized for a particular sixth-order numerical method. Summaries of extensive testing are also reported.
MSC:
65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
34K28 | Numerical approximation of solutions of functional-differential equations (MSC2010) |
65L20 | Stability and convergence of numerical methods for ordinary differential equations |
65L70 | Error bounds for numerical methods for ordinary differential equations |
65L50 | Mesh generation, refinement, and adaptive methods for ordinary differential equations |