Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

In this paper, we study the concept of statistical convergence on L?fuzzy normed spaces. Then give a useful characterization for statistically convergent sequences. Furthermore, illustrate that our method is more general than usual

This paper studies Tikhonov regularization for finitely smoothing operators in Banach spaces when the penalizationenforces too much smoothness sense that penalty term is not finite at truesolution. In a Hilbert space setting, Natterer [Applicable Anal., 18 (1984), pp. 29-37] showed with help of spectral theory optimal rates can be achieved this situation. ("Oversmoothing does harm.") For oversm...

Human's exploration of space has changed over time, depending on the expansion limits his knowledge. Space is infinite, but it limited by possibility human The original man knew very little about in which he lived - its shape, size, content, etc. Over began to take shapes that describe it. Those forms are dimensions, increased as knowledge in-creased. Knowledge spread more and more, from Earth'...

Space-time multigrid refers to the use of methods solve discretized partial differential equations considering at once multiple time steps. A new theoretical analysis is developed for case where one uses coarsening in space only. It proves bounds on 2-norm iteration matrix that connect it norm when using same method corresponding stationary problem. When properly defined wavefront type smoother...

This paper aims to present a new analysis framework for assessing disparities among regions (or countries). It combines both economic and social variables, where the economic attributes refer in particular to marked differences in consumption variables. This analysis is also appealing for spatial convergence analyses over time. In our paper, both economic and social variables are included as th...