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.
On the worst scenario method: Application to uncertain nonlinear differential equations with numerical examples
On the Zero Stability of the Variable Order Variable Stepsize BDF-Formulas.
On those ordinary differential equations that are solved exactly by the improved Euler method
As a numerical method for solving ordinary differential equations , the improved Euler method is not assumed to give exact solutions. In this paper we classify all cases where this method gives the exact solution for all initial conditions. We reduce an infinite system of partial differential equations for to a finite system that is sufficient and necessary for the improved Euler method to give the exact solution. The improved Euler method is the simplest explicit second order Runge-Kutta 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.
On Transformations of Graded Matrices, with Applications to Stiff ODE's.
One parameter family of linear difference equations and the stability problem for the numerical solution of ODEs.
One-dimensional adaptive grid generation.
One-step and Extrapolation Methods for Differential-Algebraic Systems.