On an Euler-like method with exponential correction for initial-value problems
On an interaction of two elastic bodies: analysis and algorithms
The paper deals with existence and uniqueness results and with the numerical solution of the nonsmooth variational problem describing a deflection of a thin annular plate with Neumann boundary conditions. Various types of the subsoil and the obstacle which influence the plate deformation are considered. Numerical experiments compare two different algorithms.
On approximate solution of systems of linear ordinary differential equations
On -closeness of invariant foliations under numerics.
On Calculating the Eigenvalues of the Finite Hill's Differential Equation
On Clenshaws's Method and a Generalisation to Faber Series.
On collocation methods for singular perturbation problems of convection-diffusion type.
On consistency, stability and convergence of staggered solution procedures
The simultaneous and staggered procedures of solving a partitioned form of a coupled system of ordinary differential equations are presented. Formulas for errors are compared. Counter-examples for convergence with a constant number of iterations at each time step are given.
On difference schemes for quasilinear evolution problems.
On D-stability and B-stability.
On efficient method for system of fractional differential equations.
On energy conservation of the simplified Takahashi-Imada method
In long-time numerical integration of Hamiltonian systems, and especially in molecular dynamics simulation, it is important that the energy is well conserved. For symplectic integrators applied with sufficiently small step size, this is guaranteed by the existence of a modified Hamiltonian that is exactly conserved up to exponentially small terms. This article is concerned with the simplified Takahashi-Imada method, which is a modification of the Störmer-Verlet method that is as easy to implement...
On Euler methods for Caputo fractional differential equations
Numerical methods for fractional differential equations have specific properties with respect to the ones for ordinary differential equations. The paper discusses Euler methods for Caputo differential equation initial value problem. The common properties of the methods are stated and demonstrated by several numerical experiments. Python codes are available to researchers for numerical simulations.
On Gel'fand's method of chasing for solving multipoint boundary value problems
On Generalized Linear Multistep Methods with Zero-Parasitic Roots and an Adaptive Principal Root.
On highly oscillatory problems arising in electronic engineering
In this paper, we consider linear ordinary differential equations originating in electronic engineering, which exhibit exceedingly rapid oscillation. Moreover, the oscillation model is completely different from the familiar framework of asymptotic analysis of highly oscillatory integrals. Using a Bessel-function identity, we expand the oscillator into asymptotic series, and this allows us to extend Filon-type approach to this setting. The outcome is a time-stepping method that guarantees ...
On Improving the Absolute Stability of Local Extrapolation
On Invariant Closed Curves for One-Step Methods.
On mesh independence and Newton-type methods
Mesh-independent convergence of Newton-type methods for the solution of nonlinear partial differential equations is discussed. First, under certain local smoothness assumptions, it is shown that by properly relating the mesh parameters and for a coarse and a fine discretization mesh, it suffices to compute the solution of the nonlinear equation on the coarse mesh and subsequently correct it once using the linearized (Newton) equation on the fine mesh. In this way the iteration error will be...
On multipoint boundary value problems for systems of functional-differential and difference equations.