On a finite-element collocation method which reproduces the Padé table
On a Least-Squares Collocation Method for Linear Differential-Algebraic Equations.
On a semi-variational method for parabolic equations. II
On a simulation of the oscillation excited by a random force
On an Euler-like method with exponential correction for initial-value problems
On approximate solution of systems of linear ordinary differential equations
On -closeness of invariant foliations under numerics.
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 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 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 numerical integration of implicit ordinary differential equations
In this paper it is shown how the numerical methods for ordinary differential equations can be adapted to implicit ordinary differential equations. The resulting methods are of the same order as the corresponding methods for ordinary differential equations. The convergence theorem is proved and some numerical examples are given.
On numerical solution of ordinary differential equations with discontinuities
The author defines the numerical solution of a first order ordinary differential equation on a bounded interval in the way covering the general form of the so called one-step methods, proves convergence of the method (without the assumption of continuity of the righthad side) and gives a sufficient condition for the order of convergence to be .
On Runge-Kutta, collocation and discontinuous Galerkin methods: Mutual connections and resulting consequences to the analysis
Discontinuous Galerkin (DG) methods are starting to be a very popular solver for stiff ODEs. To be able to prove some more subtle properties of DG methods it can be shown that the DG method is equivalent to a specific collocation method which is in turn equivalent to an even more specific implicit Runge-Kutta (RK) method. These equivalences provide us with another interesting view on the DG method and enable us to employ well known techniques developed already for any of these methods. Our aim will...
On simulations of the classical harmonic oscillator equation by difference equations.