On continuous interval functions
On Optimal Global Error Bounds Obtained by Scaled Local Error Estimates.
On the gap between the semilocal convergence domains of two Newton methods
We answer a question posed by Cianciaruso and De Pascale: What is the exact size of the gap between the semilocal convergence domains of the Newton and the modified Newton method? In particular, is it possible to close it? Our answer is yes in some cases. Using some ideas of ours and more precise error estimates we provide a semilocal convergence analysis for both methods with the following advantages over earlier approaches: weaker hypotheses; finer error bounds on the distances involved, and at...
On the semilocal convergence of a fast two-step Newton method.
On total truncation error estimation for the one-step method
In this paper the author establishes estimation of the total truncation error after steps in the fifth order Ruge-Kutta-Huťa formula for systems of differential equations. The approach is analogous to that used by Vejvoda for the estimation of the classical formulas of the Runge-Kutta type of the 4-th order.