Cubic Spline Colocation Methods For Several Classes Of Functional Diferential Equations

In this paper, cubic spline collocation method for initial value of ordinarydifferential equationand initial value of delay differential equationare discussed. The main results are as follows:(1)Cubic spline collocation method for ordinary differential equations is constructedin this paper. The local truncation error, convergence and consistencyare also obtained. We have also discussed linear stability of this method andobtained nonlinear stability of this method which based on Lipschitz condition.(2)Cubic spline collocation method for delay differential equations is constructedin this paper. The local truncation error, convergence and consistencyare also obtained. We have also discussed linear stability of this method andobtained nonlinear stability of this method which based on Lipschitz condition.(3)Several numerical examples have been given in this paper, the results ofwhich successfully verified the theoretical results. Besides, we have applied cubicspline method to differential equations with variable delay and neutral delay differentialequations and got some satisfied results.