A Computational Solution for a Matrix Riccati Differential Equation.
A convergence theorem on the iterative solution of nonlinear two-point boundary-value systems
Algebras of approximation sequences: Fredholm theory in fractal algebras
The present paper is a continuation of [5, 7] where a Fredholm theory for approximation sequences is proposed and some of its properties and consequences are studied. Here this theory is specified to the class of fractal approximation methods. The main result is a formula for the so-called α-number of an approximation sequence (Aₙ) which is the analogue of the kernel dimension of a Fredholm operator.
An iterative method of solving differential equations
Analog solution of a given problem in the back time
Analysis for a molten carbonate fuel cell.
Boundary value problems for the mildly non-linear ordinary differential equation of the fourth order
Cases when the use of the analytic method for solving differential equations is better than the use of numerical ones
Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations
Using the min-plus version of the spectral radius formula, one proves: 1) that the unique eigenvalue of a min-plus eigenvalue problem depends continuously on parameters involved in the kernel defining the problem; 2) that the numerical method introduced by Chou and Griffiths to compute this eigenvalue converges. A toolbox recently developed at I.n.r.i.a. helps to illustrate these results. Frenkel-Kontorova models serve as example. The analogy with homogenization of Hamilton-Jacobi equations is emphasized....
Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations
Using the min-plus version of the spectral radius formula, one proves: 1) that the unique eigenvalue of a min-plus eigenvalue problem depends continuously on parameters involved in the kernel defining the problem; 2) that the numerical method introduced by Chou and Griffiths to compute this eigenvalue converges. A toolbox recently developed at I.n.r.i.a. helps to illustrate these results. Frenkel-Kontorova models serve as example. The analogy with homogenization of Hamilton-Jacobi equations...
Difference Approximations for Singular Perturbations of Systems of Ordinary Differential Equations.
Digital simulation of analog computing differential equations with variable coefficients and nonlinear differential equations
Dynamic systems described by differential equations with singularities of the type and their machine solving
Dynamic systems with the nonzero initial conditions excited by the Dirac function
Étude mathématique d'un modèle de flamme laminaire sans température d'ignition : I - cas scalaire
Interpolation in Sobolevschen Funktionenräumen.
Inverse monotonicity and difference schemes of higher order. A summary for two-point boundary value problems.
Linear distributional differential equations of the second order
The paper deals with the linear differential equation (0.1) with distributional coefficients and solutions from the space of regulated functions. Our aim is to get the basic existence and uniqueness results for the equation (0.1) and to generalize the known results due to F. V. Atkinson [At], J. Ligeza [Li1]-[Li3], R. Pfaff ([Pf1], [Pf2]), A. B. Mingarelli [Mi] as well as the results from the paper [Pe-Tv] concerning the equation (0.1).
Local convergence analysis for a certain class of inexact methods.
Newton's Method Under Mild Differentiability Conditions with Error Analysis.