  This article is concerned with the derivation of numerical reconstruction
schemes for the inverse moving source problem on determining source profiles in
(time-fractional) evolution equations. As a continuation of the theoretical
result on the uniqueness, we adopt a minimization procedure with regularization
to construct iterative thresholding schemes for the reduced backward problems
on recovering one or two unknown initial value(s). Moreover, an elliptic
approach is proposed to solve a convection equation in the case of two
profiles.
