Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces

In this paper, we propose a generalized viscosity implicit iterative method for asymptotically non-expansive mappings in Banach spaces. The strong convergence theorem of this algorithm is proved, which solves the variational inequality problem. Moreover, we provide some applications to zero-point problems and equilibrium problems. Further, a numerical example is given to illustrate our convergence analysis. The results generalize and improve corresponding results in the literature.

Low-Speed Preconditioning for AUSM+-Up Scheme

Based on Navier-stokes equations, Weiss-Smith matrix preconditioning method is implemented within pseudo time derivative term. AUSM+-up family schemes and LU-SGS implicit iterative method were used to solve low speed flows and were compared with literature data and theoretical value. Through comparing calculation with the literature data and theoretical value, The results showed the preconditioning algorithm can be applied efficiently to the low speeds flow field, All these works built foundations for further application of chemical flows.

Study Method for Low Speed Flow Basic on Precondition

Based on Navier-stokes equations, Weiss-Smith matrix preconditioning method is implemented within pseudo time derivative term. AUSM+-up family schemes and LU-SGS implicit iterative method were used to solve low speed flows and were compared with literature data and theoretical value. Through comparing calculation with the literature data and theoretical value, The Results showed the preconditioning algorithm can be applied efficiently to the low speeds flow field ,All these works built foundations for further application of chemical flows.

Implicit Iterative Method for Hierarchical Variational Inequalities

We introduce a new implicit iterative scheme with perturbation for finding the approximate solutions of a hierarchical variational inequality, that is, a variational inequality over the common fixed point set of a finite family of nonexpansive mappings. We establish some convergence theorems for the sequence generated by the proposed implicit iterative scheme. In particular, necessary and sufficient conditions for the strong convergence of the sequence are obtained.