Numerical Stability Of Parallel Rosenbrock Method And Block θ-Method For Delay Differential Equations

In this paper, we focus on the parallel Rosenbrock methods of delay differential equations and the stability of a linear neutral delay-integro-differential equation.First, we present numerical stability theory of delay differential equations and parallel methods.Second,based on the demand of practical numerical simulation and scientific computation, and aimed at stiffly large systems, this paper presents a class of parallel Rosenbrock methods implemented on a shared-memory MIMD multicomputer. Parallel Rosenbrock methods are obtaind. The different internal stages of Rosenbrock methods are calculated in parallel on different processors. Second, the method applied on delay differential equations. Its stability and convergence were studied. This method has better stability. It doesn't need iteration.Immediately after, in this paper our main emphasis is to study the stability of the blockθ-method for linear neutral Volterra delay-integro-differential system. Futhermore, it is proved that numerical solutions preserves the delay independent stability of its exact solutions. Finally, the numerical experiments are given to demonstrate the conclusions.