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.
On the solution of a differential equation occurring in the problem of heat convection in laminar flow through a tube with slip-flow.
On the solution of linear algebraic systems arising from the semi–implicit DGFE discretization of the compressible Navier–Stokes equations
We deal with the numerical simulation of a motion of viscous compressible fluids. We discretize the governing Navier–Stokes equations by the backward difference formula – discontinuous Galerkin finite element (BDF-DGFE) method, which exhibits a sufficiently stable, efficient and accurate numerical scheme. The BDF-DGFE method requires a solution of one linear algebra system at each time step. In this paper, we deal with these linear algebra systems with the aid of an iterative solver. We discuss...
On the Stability of Backward Differentiation Methods.
On the stability of solutions of a multipoint boundary value problem for a system of generalized ordinary differential equations.
On the Stability of the Ritz Procedure for Nonlinear Problems.
On the stability of the Ritz procedure for nonlinear two-point boundary value problems
On the Stability Properties of Brown's Multistep Multiderivative Methods.
On the Structure of Error Estimates for Finite-Difference Methods.
On the tangential velocity arising in a crystalline approximation of evolving plane curves
In a crystalline algorithm, a tangential velocity is used implicitly. In this short note, it is specified for the case of evolving plane curves, and is characterized by using the intrinsic heat equation.
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 worst scenario method: a modified convergence theorem and its application to an uncertain differential equation
We propose a theoretical framework for solving a class of worst scenario problems. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. The main convergence theorem modifies and corrects the relevant results already published in literature. The theoretical framework is applied to a particular problem with an uncertain boundary value problem for a nonlinear ordinary differential equation with an uncertain coefficient.