Exponential functions as boundary layer functions.
Feedback and Adaptive Finite Element Solution of One-Dimenional Boundary Value Problems.
Finite Difference Methods and Their Convergence for a Class of Singular Two Point Boundary Value Problems.
Galerkin-wavelet methods for two-point boundary value problems.
Gaussian collocation via defect correction.
Gaussian quadrature rules and -stability of Galerkin schemes for ODE.
General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators
This paper is concerned with an extension and reinterpretation of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. We state two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then these results are applied to Dirac operators in order to characterize simultaneously eigenvalues corresponding to electronic and positronic bound states.
Global error control for the continuous Galerkin finite element method for ordinary differential equations
Globale Superkonvergenz bei der Lösung von linearen Randwertaufgaben.
Improvement of Numerical Solution of Boundary Layer Problems by Incorporation of Asymptotic Approximations.
La résolution numérique des problèmes différentiels aux conditions initiales par des méthodes de collocation
Local interpolation by a quadratic Lagrange finite element in 1D
We analyse the error of interpolation of functions from the space in the nodes of a regular quadratic Lagrange finite element in 1D by interpolants from the local function space of this finite element. We show that the order of the error depends on the way in which the mutual positions of nodes change as the length of interval approaches zero.
Lower Norm Estimates for Approximate Solutions of Differential Equations with Non-Smooth Coefficients.
Maximale Konvergenzordnung bei der numerischen Lösung von Anfangswertproblemen mit Splines.
Minimum principle for quadratic spline collocation discretization of a convection-diffusion problem
New algorithm for the numerical solutions of nonlinear third-order differential equations using Jacobi-Gauss collocation method.
Numerical Approximations of the Relative Rearrangement: The piecewise linear case. Application to some Nonlocal Problems
We first prove an abstract result for a class of nonlocal problems using fixed point method. We apply this result to equations revelant from plasma physic problems. These equations contain terms like monotone or relative rearrangement of functions. So, we start the approximation study by using finite element to discretize this nonstandard quantities. We end the paper by giving a numerical resolution of a model containing those terms.
Numerical solution of a 1-d elastohydrodynamic problem in magnetic storage devices
In this work we present new numerical methods to simulate the mechanics of head-tape magnetic storage devices. The elastohydrodynamic problem is formulated in terms of a coupled system which is governed by a nonlinear compressible Reynolds equation for the air pressure over the head, and a rod model for the tape displacement. A fixed point algorithm between the solutions of the elastic and hydrodynamic problems is proposed. For the nonlinear Reynolds equation, a characteristics method and a...
Numerical solution of second order one-dimensional linear hyperbolic equation using trigonometric wavelets
A numerical technique is presented for the solution of second order one dimensional linear hyperbolic equation. This method uses the trigonometric wavelets. The method consists of expanding the required approximate solution as the elements of trigonometric wavelets. Using the operational matrix of derivative, we reduce the problem to a set of algebraic linear equations. Some numerical example is included to demonstrate the validity and applicability of the technique. The method produces very accurate...
Numerische Stabilität des Ritzschen Verfahrens