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Convergence theorems for iterative Runge-Kutta methods with a constant integration step

Kulikov, Gennady Yu

Computational Mathematics and Mathematical Physics, 36(8) (1996), 1041-1054

Numerical methods for solving Cauchy's problem for a system of differential-algebraic equations constructed by implicit Runge-Kutta methods using methods such as simple iteration, the modified Newton's method and Newton's method are considered. Convergence theorems for these combined methods are proved and estimates for the accuracy of the solution are obtained. The theoretical results are confirmed by numerical examples.