  In the theory and practice of inverse problems for partial differential
equations (PDEs) much attention is paid to the problem of the identification of
coefficients from some additional information. This work deals with the problem
of determining in a multidimensional parabolic equation the lower coefficient
that depends on time only. To solve numerically a nonlinear inverse problem,
linearized approximations in time are constructed using standard finite element
procedures in space. The computational algorithm is based on a special
decomposition, where the transition to a new time level is implemented via
solving two standard elliptic problems. The numerical results presented here
for a model 2D problem demonstrate capabilities of the proposed computational
algorithms for approximate solving inverse problems.
