Iterative identification of the spacewise-dependent right-hand side in a parabolic equation

The problem of determining a spacewise-dependent right-hand side in a one-dimensional parabolic equation is considered. The method of conjugate gradients in combination with the method of finite differences with implicit time approximation with the weighting factor $\sigma\in[0, 1]$ is used for the numerical solution of the inverse initial-boundary value problem. The effectiveness of the proposed computational algorithm is confirmed by the results of the computational experiment for model problems with quasi-real solutions, including problems with overdetermination conditions having random errors.