Yagoub, Hemza2013-11-072013-11-0720092009Source: Masters Abstracts International, Volume: 48-01, page: 0431.http://hdl.handle.net/10393/28075http://dx.doi.org/10.20381/ruor-12376This 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.77 p.enMathematics.Thesis