Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

A broadcast authentication and integrity augmentation for trusted differential GPS in marine navigation

In this paper we propose an efficient authentication and integrity scheme to support DGPS corrections using the RTCM protocol, such that the identified vulnerabilities in DGPS are mitigated. The proposed scheme is based on the TESLA broadcast protocol with modifications that make it suitable for the bandwidth and processor constrained environment of marine DGPS.