Variable-step variable-order 3-stage Hermite-Birkhoff ODEDDE solver of order 5 to 15

Abstract

This thesis presents the variable-step variable-order 3-stage Hermite-Birkhoff numerical solver HB515DDE of order 5 to 15. This method can solve ordinary and delay differential equations (ODEs/DDEs) with state-dependent, non-vanishing, small, vanishing and asymptotically vanishing delays. Delayed values are computed using Hermite interpolation and small delays are dealt with using extrapolation. Discontinuities in DDEs are located by a bisection method. HB515DDE was tested and compared with other solvers. The results are given along with the convergence theory which supports the experimentation.