Continuous block implicit hybrid one-step methods for ordinary and delay differential equations

A class of high order continuous block implicit hybrid one-step methods has been proposed to solve numerically initial value problems for ordinary and delay differential equations. The convergence and Aω-stability of the continuous block implicit hybrid methods for ordinary differential equations are studied. Alternative form of continuous extension is constructed such that the block implicit hybrid one-step methods can be used to solve delay differential equations and have same convergence order as for ordinary differential equations. Some numerical experiments are conducted to illustrate the efficiency of the continuous methods.