A reliable error estimation for diagonally implicit multistage integration methods (Q5960906)

The class of diagonally implicit multistage integration methods (DIMSIMs) on a nonuniform mesh is introduced to solve autonomous ordinary differential equations on a compact interval. Then a new approach to estimate the local discretization error is presented. The error constant of the main error term is calculated explicitely and depends on the ratio of consecutive step sizes. Moreover, estimators of local discretization errors based on this representation are derived. Finally these error estimators are tested and compared with former estimators derived by the authors. In numerical test examples it is shown, that in contrast to the former error estimators, the present ones give a reliable estimation for any step size pattern.