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In the paper, we study the elliptical type equation with strongly changing coefficients. We are interested in studying such equation because the given type equations are yielded when we use the fictitious domain method. In this paper we suggest a special method for numerical solution of the elliptic equation with strongly changing coefficients. We have proved the theorem for the assessment of developed iteration process convergence rate. We have developed computational algorithm and numerical calculations have been done to illustrate the effectiveness of the suggested method.

Sedimentation process as the form of iteration process has been studied using fractal statistics in the case of the change of Hurst exponent patterns. The similar profile of Hurst exponent can be related to the one depositional cycle, which can be explained that the fractal statistics might detect the sedimentation process in one interval time. Models that showed the effect of the chosen time lag have been presented. The time lag affects the effectively of fractal statistics in determining the stratification of sedimentary rocks. In this study, we modeled resistivity layer and 1/f noise is added to the resistivity values for each layer. We calculated Hurst exponent with different window length. We observed that the layer boundaries can be distinguished from the Hurst exponent. From our models, we obtained that the window length affects the fractal statistics in detection of top layer. Large window length hardly detects thin layer and accurately enough in detection of thick layers as shown in three isotropic layers model. Small window length is accurately enough in detecting the changes on layers although it also reflects the scaling behavior of the noise. The models show that when window length increases the correlation continues decreasing and becomes uncorrelated when window length infinite.

In this paper, we apply a new three-step iteration process into a CAT(0) space and present some results on the strong and Δ-convergence of the new three-step iteration for generalized nonexpansive mappings in a CAT(0) space. Our results extend and improve some results in the literature.