A method of error analysis for Runge-Kutta methods (Q1571262)

The author develops a new method for controlling the integration step in Runde-Kutta methods. In contrast to the classical one, the proposed method of error analysis for the numerical solution of ordinary differential equations is based on the global error, rather than on the local one, which is more important for the accuracy of solution. It is shown that the proposed method of controlling the numerical integration step is particularly efficient as applied to implicit Runge-Kutta method. Estimates are given for numbers of iteration steps in the complete and modified Newton method that are required for a correct use of iterative approximations in the procedure of controlling the global error.