SIM Talk: Sean Kelly

Short Abstract: 

In this talk, we will introduce some of the basic ideas of fractional calculus which involve differential and integral operators of non-integer order. Then, an initial-boundary value, subdiffusion problem involving a Caputo time derivative of fractional order will be considered. The solutions of which typically exhibit a singular behaviour at initial time, . We propose an extension to the approach, by Kopteva [1], used to analyse the error of L1-type discretizations on both graded and uniform temporal meshes. We also broaden the assumption on the regularity of the solution to incorporate a more general parameter, , such that .

[1] Natalia Kopteva. Error analysis for time-fractional semilinear parabolic equations using upper and lower solutions. SIAM J. Numer. Anal. 58, 2020