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Byline: Treena. Basu, Sebastian. Engel-Wolf, Olaf. Menzer Advances in Machine Learning and availability of state-of-the-art computational resources, along with digitized healthcare data, have set the stage for extensive application of [...]

Byline: Kanadpriya. Basu, Ritwik. Sinha, Aihui. Ong, Treena. Basu Artificially intelligent computer systems are used extensively in medical sciences. Common applications include diagnosing patients, end-to-end drug discovery and development, improving [...]

Fractional diffusion equations provide an adequate and accurate description of transport processes that exhibit anomalous diffusion that cannot be modeled accurately by classical second-order diffusion equations. However, numerical discretizations of fractional diffusion equations yield full coefficient matrices, which require a computational operation of O(N3) per time step and a memory of O(N2) for a problem of size N. In this paper we develop a fast second-order finite difference method for space-fractional diffusion equations, which only requires memory of O(N) and computational work of O(N log2 N). Numerical experiments show the utility of the method. [ABSTRACT FROM AUTHOR]