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In a second part, we address the numerical resolution of the problem by using a descent method with projection and optimal step-size parameter.
In the numerical study, the three dimensional governing equations were solved by finite difference method with projection algorithm using FORTRAN programming language.
In the numerical part of the study, incompressible Navier Stokes equations, derived from an orthogonal helical coordinate system were solved by finite difference method with projection algorithm using FORTRAN programming language.
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The incompressible smoothed particle hydrodynamics (ISPH) method with projection-based pressure correction has been shown to be highly accurate and stable for internal flows and, importantly for many problems, the pressure field is virtually noise-free in contrast to the weakly compressible SPH approach (Xu et al., 2009 [31]).
Hereafter, we use 3D-CSR-I/3D-LCSR-I to denote the routing methods with Projection Method 1 (mapping nodes on a 3D sphere) and 3D-CSR-II/3D-LCSR-II to denote the routing methods with Projection Method 2 (mapping nodes on a 4D sphere).
Data maps from both methods, together with projection intervals from the probabilistic method, offer enhanced ways to communicate the potential variation in landscape simulation.
In 2005, Matsushita and Takahashi [8] proposed the following hybrid iteration method with generalized projection for relatively nonexpansive mapping in a Banach space : (1.10).
In 2007, Qin and Su [2] proposed the following hybrid iteration method with generalized projection for relatively nonexpansive mapping in a Banach space : (1.2).
In 2005, Shin-ya Matsushita and Wataru Takahashi [1] proposed the following hybrid iteration method (it is also called the CQ method) with generalized projection for relatively nonexpansive mapping in a Banach space : (1.1).
In 2005, Matsushita and Takahashi [18] proposed the following hybrid iteration method (it is also called the CQ method) with generalized projection for relatively nonexpansive mapping in a Banach space : chosen arbitrarily, (1.3).
In 2009, Zhou et al. [11] proposed the following modification of the hybrid iteration method with generalized projection for a family of closed and quasi- -asymptotically nonexpansive mappings in a Banach space : (1).
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