On the convergence of multistep methods for nonlinear stiff differential equations.
On the Design of High Order Exponentially Fitted Formulae for the Numerical Integration of Stiff Systems.
On the discretization of a partial differential equation in the neighborhood of a periodic orbit.
On the Estimation of Errors Propagated in the Numerical Integration of Ordinary Differential Equations.
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 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 Relation Between Algebraic Stability and B-Convergence for Runge-Kutta Methods.
On the Stability of Backward Differentiation Methods.
On the Stability Properties of Brown's Multistep Multiderivative Methods.
On the Uniform Power-Boundedness of a Family of Matrices and the applications to One-Leg and Linear Multistep Methods.
On the unique solvability of the Runge-Kutta equations.
On the Zero Stability of the Variable Order Variable Stepsize BDF-Formulas.
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.
On Transformations of Graded Matrices, with Applications to Stiff ODE's.