On the multi-grid iteration for the eigenvalue problem and the degree of interpolation wich it requires (I).
On the Multigrid Solution of Finite Element Equations With Isoparametric Elements.
On the Multi-Level Splitting of Finite Element Squares.
On the necessary and sufficient conditions for the convergence of the difference schemes for the general boundary value problem for the linear systems of ordinary differential equations
We consider the numerical solvability of the general linear boundary value problem for the systems of linear ordinary differential equations. Along with the continuous boundary value problem we consider the sequence of the general discrete boundary value problems, i.e. the corresponding general difference schemes. We establish the effective necessary and sufficient (and effective sufficient) conditions for the convergence of the schemes. Moreover, we consider the stability of the solutions of general...
On the Newton-Kantorovich theorem and nonlinear finite element methods
Using a weaker version of the Newton-Kantorovich theorem, we provide a discretization result to find finite element solutions of elliptic boundary value problems. Our hypotheses are weaker and under the same computational cost lead to finer estimates on the distances involved and a more precise information on the location of the solution than before.
On the nodal set of eigenfunctions
On the nomographic chart of three complex variables in the line coordinates
The author investigates methods of nomographing functional relations among three complex variables which satisfy the equation (involving Massau’s complex chart determinant) det , in the line coordinates.
On the nonlinear implicit complementarity problem.
On the notion of Jacobi fields in constrained calculus of variations
In variational calculus, the minimality of a given functional under arbitrary deformations with fixed end-points is established through an analysis of the so called second variation. In this paper, the argument is examined in the context of constrained variational calculus, assuming piecewise differentiable extremals, commonly referred to as extremaloids. The approach relies on the existence of a fully covariant representation of the second variation of the action functional, based on a family of...
On the Number of Best Approximations in Certain Non-Linear Families of Functions. (Short Communication).
On the number of iterations required by Von Neumann addition
We investigate the number of iterations needed by an addition algorithm due to Burks et al. if the input is random. Several authors have obtained results on the average case behaviour, mainly using analytic techniques based on generating functions. Here we take a more probabilistic view which leads to a limit theorem for the distribution of the random number of steps required by the algorithm and also helps to explain the limiting logarithmic periodicity as a simple discretization phenomenon.
On the number of iterations required by Von Neumann addition
We investigate the number of iterations needed by an addition algorithm due to Burks et al. if the input is random. Several authors have obtained results on the average case behaviour, mainly using analytic techniques based on generating functions. Here we take a more probabilistic view which leads to a limit theorem for the distribution of the random number of steps required by the algorithm and also helps to explain the limiting logarithmic periodicity as a simple discretization phenomenon.
On the Numerical Analysis of the Von Karman Equations : Mixed Finite Element Approximation and Continuation Techniques.
On the Numerical Approximation of Finite Speed Diffusion Problems.
On the numerical approximation of first-order Hamilton-Jacobi equations
Some methods for the numerical approximation of time-dependent and steady first-order Hamilton-Jacobi equations are reviewed. Most of the discussion focuses on conformal triangular-type meshes, but we show how to extend this to the most general meshes. We review some first-order monotone schemes and also high-order ones specially dedicated to steady problems.
On the numerical computation of slowly convergent series.
On the Numerical Errors in One Step Algorithms for Time Dependent Problems.
On the Numerical Evaluation of a Sum Involving Binomial Coefficients.
On the Numerical Integration of the Heat Equation.
On the numerical modeling of deformations of pressurized martensitic thin films
We propose, analyze, and compare several numerical methods for the computation of the deformation of a pressurized martensitic thin film. Numerical results have been obtained for the hysteresis of the deformation as the film transforms reversibly from austenite to martensite.