HONORS SENIOR  COMPS PRESENTATION

in Mathematics

A Fast Solution Method for Space Fractional Diffusion Equations

 

Greg Capra

Fractional diffusion equations have been proven to accurately model Anomalous diffusion processes in nature. However, these equations are resolved to matrices with computational complexity and storage capacity \( {\cal O}(N^3) \) and \( {\cal O}(N^2) \) respectively, which is increasingly problematic for larger N. I will provide a fast, efficient, and accurate algorithm for numerically approximating the solution to these discretized diffusion equations by utilizing the Crank-Nicolson scheme together with well-known matrix manipulation techniques