CONTINUOUS BLOCK θ-METHODS FOR ORDINARY AND DELAY DIFFERENTIAL EQUATIONS

Continuous numerical methods have many applications in the numerical solution of discontinuous ordinary differential equations (ODEs), delay differential equations, neutral differential equations, integro-differential equations, etc. This paper deals with a continuous extension for the discrete approximate solution of ODEs generated by a class of block theta-methods. Existence and uniqueness for the continuous extension are discussed. Convergence and absolute stability of the continuous block theta-methods for ODEs are studied. As an application, we adopt the continuous block.-methods to solve delay differential equations and prove that the continuous block theta-methods are GP-stable if and only if they are A(omega)-stable for ODEs. Several numerical experiments are given to illustrate the performance of the continuous block theta-methods.