In this paper, we introduce a new parameter iteration method (P-Iteration for short) ,which can be applied on Adams-Moulton methods to solve initial value problems. Compared with Jacobi iteration method, it has three advantages: (1) it may significantly implement the stable region of the iterative process such that we can efficiently use the large stable region of implicit formula; (2) it allow...

We apply a Runge-Kutta-based waveform relaxation method to initial-value problems for implicit differential equations. In the implementation of such methods, a sequence of nonlinear systems has to be solved iteratively in each step of the integration process. The size of these systems increases linearly with the number of stages of the underlying Runge-Kutta method, resulting in high linear alg...

The purpose of this paper is to introduce an implicit iterative process with errors for approximating common fixed point of two finite families of asymptotically nonexpansive mappings in the framework of Banach space. The results presented in this paper extend and generalize the corresponding results of Qin et al.[Convergence analysis of implicit iterative algorithms for asymptotically nonexpan...

The purpose of this paper is to introduce an implicit iteration process for approximating common fixed points of two asymptotically nonexpansive mappings and to prove strong convergence theorems in uniformly convex Banach spaces.