Convergence and Stability in Collocation Methods of Equation u ′ ( t ) = a u ( t ) + b u ( [ t ] )

Abstract

This paper is concerned with the convergence, global superconvergence, local superconvergence, and stability of collocation methods for $u^{\prime }(t)=au(t)+bu([t])$. The optimal convergence order and superconvergence order are obtained, and the stability regions for the collocation methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained, and some numerical experiments are given.