**Determination of a Time-Dependent Term in the Right-Hand Side of Linear Parabolic Equations **

* Nguyen Thi Ngoc Oanh, Bui Viet Huong *

**Abstract**

The problem of determining a time-dependent term from integral observations in the right-hand side of parabolic equations is studied. It is reformulated into a variational problem, and a formula for the gradient of the functional to be minimized is derived via an adjoint problem. The variational problem is discretized by the splitting method based on finite differences. A formula for the gradient of the discretized functional is given and the conjugate gradient method is suggested for numerically solving the problem. Several numerical examples are presented for illustrating the efficiency of the algorithm.