Общие линейные блочные многошаговые методы решения задачи Коши для обыкновенных дифференциальных уравнений

Abstract

Generalized block multistage methods for solving of Cauchy problem for ordinary differential equations systems are described. Formulas for general m- steps k-points block methods are obtained, their precision order is determined. Convergence conditions by Dalquist are determined. Convergence of stabled by initial datum general m-steps k-points block methods is proved. A priori error estimation of approximate solution is obtained. Example of Cauchy problem solution by double-step two- point block method is given. Obtained results allow to build the new more effectiveness parallel algorithms and their application for modern multiprocessor computing systems