Simulation of a space-time bounded diffusion

Space–time fractional diffusion on bounded domains

Time-Bounded and Space-Bounded Sensing in Wireless Sensor Networks

Most papers on sensing in wireless sensor networks use only very simple sensors, e.g. humidity or temperature, to illustrate their concepts. However, in a large number of scenarios including structural health monitoring, more complex sensors that usually employ medium to high frequency sampling and post-processing are required. Additionally, to capture an event completely several sensors of dif...

Space-time radial basis function collocation method for one-dimensional advection-diffusion problem

The parabolic partial differential equation arises in many application of technologies. In this paper, we propose an approximate method for solution of the heat and advection-diffusion equations using Laguerre-Gaussians radial basis functions (LG-RBFs). The results of numerical experiments are compared with the other radial basis functions and the results of other schemes to confirm the validit...

Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation.

We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Lévy alpha -stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler...

An Implicit Difference-ADI Method for the Two-dimensional Space-time Fractional Diffusion Equation

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...