On the error estimation in numerical methods
On the Estimation of Errors Propagated in the Numerical Integration of Ordinary Differential Equations.
On the existence of solutions and one-step method for functional-differential equations with parameters
On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate
In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of the algebraic...
On the Integration of Stiff Systems of O.D.E.s Using Extended Backward Differentiation Formulae.
On the iterative inclusion of solutions in initial value problems
On the necessary and sufficient conditions for the convergence of the difference schemes for the general boundary value problem for the linear systems of ordinary differential equations
We consider the numerical solvability of the general linear boundary value problem for the systems of linear ordinary differential equations. Along with the continuous boundary value problem we consider the sequence of the general discrete boundary value problems, i.e. the corresponding general difference schemes. We establish the effective necessary and sufficient (and effective sufficient) conditions for the convergence of the schemes. Moreover, we consider the stability of the solutions of general...
On the numerical solution of implicit two-point boundary-value problems
On the numerical solution of the diffusion equation with a nonlocal boundary condition.
On the Numerical Treatment of a Small Divisor Problem.
On the Optimum Choice of Weight Functions in a Class of Variational Calculations.
On the Order Conditions of Runge-Kutta Methods with Higher Derivatives.
On the Order of Composite Multistep Methods for Ordinary Differential Equations.
On the Order of Iterated Defect Correction. An Algebraic Proof.
On the possibility of calculation of zero points of solutions of differential equations of the second order
On the Possibility of Two-Sided Error Bounds in the Numerical Solution of Initial Value Problems.
On the Reduction of Holt's Problem to a Finite Interval.
On the Relation Between Algebraic Stability and B-Convergence for Runge-Kutta Methods.
On the resonance problem for the order ordinary differential equations, Fučík’s spectrum
On the sharpness of a superconvergence estimate in connection with one-dimensional Galerkin-methods.