Numerical Error Bounds for Fourth Order Boundary Value Problems, Simultaneous Estimation of u(x) and u"(x).
Numerical integration of differential equations in the presence of first integrals: observer method
We introduce a simple and powerful procedure-the observer method-in order to obtain a reliable method of numerical integration over an arbitrary long interval of time for systems of ordinary differential equations having first integrals. This aim is achieved by a modification of the original system such that the level manifold of the first integrals becomes a local attractor. We provide a theoretical justification of this procedure. We report many tests and examples dealing with a large spectrum...
On a certain class of always convergent sequences and the Rayleigh quotient iterations
On a finite-element collocation method which reproduces the Padé table
On approximate solution of systems of linear ordinary differential equations
On Generalized Linear Multistep Methods with Zero-Parasitic Roots and an Adaptive Principal Root.
On the Approximation of Periodic Solutions of Equations with Bounded Nonlinearities.
On the Concepts of Convergence, Consistency, and Stability in Connection with some Numerical Methods.
On the existence of solutions and one-step method for functional-differential equations with parameters
On the Possibility of Two-Sided Error Bounds in the Numerical Solution of Initial Value Problems.
Overimplicit multistep methods
Point fixe d'une application non contractante.
We study a multilinear fixed-point equation in a closed ball of a Banach space where the application is 1-Lipschitzian: existence, uniqueness, approximations, regularity.
Psi-series of quadratic vector fields on the plane.
Psi-series (i.e., logarithmic series) for the solutions of quadratic vector fields on the plane are considered. Its existence and convergence is studied, and an algorithm for the location of logarithmic singularities is developed. Moreover, the relationship between psi-series and non-integrability is stressed and in particular it is proved that quadratic systems with psi-series that are not Laurent series do not have an algebraic first integral. Besides, a criterion about non-existence of an analytic...
Runge-Kutta-Verfahren mit festen und variablen Parametern zur Lösung von Systemen gewöhnlicher Differentialgleichungen 1. Ordnung
Sobolev type inequalities for p>0
Stability and local error of difference methods for the solution of the ordinary differential equation of the first order
Stability of the Rayleigh-Ritz Procedure for Nonlinear Two-Point Boundary Value Problems.
Une remarque sur l'équation des erreurs dans la solution approximative des équations différentielles
К теории вырожденных систем обыкновенных дифференциальных уравнений.
Локальный метод в нелинейных резонансах