Numerical methods improve accuracy and efficiency in modeling transport in biological tissues, suggesting advances in computational techniques.
Key Points
The aim is to develop a numerical method for time-space fractional diffusion that effectively models anomalous transport in heterogeneous biological tissues.
Developed a fully discrete numerical method integrating heterogeneous diffusion coefficients.
Utilized finite element approximation of a spectral fractional elliptic operator.
Employed an implicit L1 discretization of the Caputo derivative.
Applied a sum-of-exponentials approximation of the memory kernel.
Established unconditional stability and error estimates.
Reduced memory complexity from O(N) to O(logN) without sacrificing accuracy.
Confirmed theoretical convergence rates through numerical experiments.
Demonstrated stable behavior in all tested configurations.
Illustrated the effect of heterogeneous coefficients on transport dynamics.