A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick’s law. In this paper we combine the forward time centered space (FTCS) method, well k...

Within the context of seismic wave propagation, fractures can be described as thin layers or linear-slip interfaces. In this paper, numerical simulations of elastic wave propagation in a medium with a single fracture represented by these two models are performed by 2D finite-difference codes: a variable-grid isotropic code for the thin-layer model and a regular-grid anisotropic code for the lin...

Wavelet analysis provides information on the energy present at various scales and locations throughout a computational domain. This information is precisely the information that is needed to define the appropriate gridpoint densities and the appropriate numerical order to resolve the physics at hand in the computationally most efficient manner. Here a two-dimensional version of the numerical me...

We study a 3D bicrystal containing an axially symmetric shrinking grain which is initially a spherical segment attached along a circular groove root to the flat exterior surface of the second grain. Following Mullins [1]-[3], a time dependent problem is formulated for the coupled motion of the grain boundary, the groove root, and the external surface. Numerical solutions calculated using an imp...

Earth is inhomogeneous, which means its elastic characteristics change with depth. The seismic method employs the propagation of waves throughout the earth to locate different structures and stratigraphy. Understanding the wave propagation is an important matter in exploration seismology; therefore modeling of seismic wave is an important tool. To validate the interpreted earth model out of the...

This paper deals with numerical solution to the multi-term time fractional diffusion equation in a finite domain. An implicit finite difference scheme is established based on Caputo’s definition to the fractional derivatives, and the upper and lower bounds to the spectral radius of the coefficient matrix of the difference scheme are estimated, with which the unconditional stability and converge...

The motion of an incompressible, viscous rotating fluid contained in a spheroidal container is studied by a direct numerical simulation in an oblate spheroidal coordinate system. An appropriate formalism is first derived which allows us to expand any scalar field in spherical harmonics and to decompose any vector field into its sphero-poloidal and sphero-toroidal scalar parts. The spinover mode...

In this paper, we describe a comparison of two spatial discretization schemes for the advection equation, namely the first finite difference method and the method of lines. The stability of the methods has been studied by Von Neumann method and with the matrix analysis. The methods are applied to a number of test problems to compare the accuracy and computational efficiency. We show that both d...

We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x > 0, t > 0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and time-like boundaries, with either second or fourth order accuracy. These discrete boundary conditions suggest a general prescription for boundary conditi...

In this paper, we implement the radial basis functions for solving a classical type of time-fractional telegraph equation defined by Caputo sense for ð1oαr2Þ. The presented method which is coupled of the radial basis functions and finite difference scheme achieves the semi-discrete solution. We investigate the stability, convergence and theoretical analysis of the scheme which verify the validi...