Unsteady corrector method for accuracy analysis of linear semidiscrete schemes

Unsteady corrector method is used to find the order of accuracy when it is greater than the order of truncation error and investigate the long-time evolution of solution error. In this paper this method is applied to linear semidiscrete schemes, which allows to simplify its description. We alsopresent its generalization for schemes with matrices next to temporal derivatives. Using this method we obtain new accuracy estimates for 4-point difference scheme R3.