Other Applied Mathematics Commons^™

The tempered fractional diffusion equation is a generalization of the standard fractional diffusion equation that includes the truncation effects inherent to finite-size physical domains. As such, that equation better describes anomalous transport processes occurring in realistic complex systems. To broaden the range of applicability of tempered fractional diffusion models, efficient numerical methods are needed to solve the model equation. In this work, we have developed a pseudospectral scheme to discretize the space-time fractional diffusion equation with exponential tempering in both space and time. The model solution is expanded in both space and time in terms of Chebyshev polynomials and the …

One of the ongoing issues with fractional diffusion models is the design of an efficient high order numerical discretization. This is one of the reasons why fractional diffusion models are not yet more widely used to describe complex systems. In this paper, we derive a radial basis functions (RBF) discretization of the one-dimensional space-fractional diffusion equation. In order to remove the ill-conditioning that often impairs the convergence rate of standard RBF methods, we use the RBF-QR method [1,33]. By using this algorithm, we can analytically remove the ill-conditioning that appears when the number of nodes increases or when basis functions …