In this paper we define a finite difference method for the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic. The homogeneous boundary conditions for velocity, microrotation and heat flux are proposed. The sequence of approximate solutions for our problem is constructed by using the def...

In this paper, we present numerical procedures to compute solutions of partial differential equations posed on fractals. particular, consider the strong form equation using standard graph Laplacian matrices and also weak forms derived length or área measure a discrete approximation fractal set. We then introduce procedure normalize obtained diffusions, that is, way renormalization constant need...

II. Foundations 5 A. The Mathematical Structure of Physical Field Theories . . . 5 B. Geometric Objects and Orientation . . . . . . . . . . . . . 7 C. Physical Laws and Physical Quantities . . . . . . . . . . . . 15 D. Classification of Physical Quantities . . . . . . . . . . . . . 21 E. Topological Laws . . . . . . . . . . . . . . . . . . . . . . . 26 F. Constitutive Relations . . . . . . . . ...

In this paper we develop finite difference schemes for elliptic problems with piecewise continuous coefficients that have (possibly huge) jumps across fixed internal interfaces. contrast such involving one smooth non-intersecting interface, been extensively studied, there are very few papers addressing interface intersecting interfaces of coefficient jumps. It is well known if the values permea...