Search results for "Mathematica"
showing 10 items of 7971 documents
On finite element approximation of the gradient for solution of Poisson equation
1981
A nonconforming mixed finite element method is presented for approximation of ?w with Δw=f,w| r =0. Convergence of the order $$\left\| {\nabla w - u_h } \right\|_{0,\Omega } = \mathcal{O}(h^2 )$$ is proved, when linear finite elements are used. Only the standard regularity assumption on triangulations is needed.
Iterative approximation to a coincidence point of two mappings
2015
In this article two methods for approximating the coincidence point of two mappings are studied and moreover, rates of convergence for both methods are given. These results are illustrated by several examples, in particular we apply such results to study the convergence and their rate of convergence of these methods to the solution of a nonlinear integral equation and of a nonlinear differential equation.
On optimal estimates for the solutions of linear difference equations on the circle
1976
A linear difference equation arising in the proof of Moser's twist mapping theorem is solved and optimal estimates for the solution are established.
Navigationsformel zu A. Busemanns Variationsproblem der Raumfahrt
1970
Die Indikatrix des Variationsproblems wird auser durch die Storungsdifferentialgleichung fur die grose Halbachse und die Exzentrizitat durch einen Zusammenhang zwischen der Richtung des Impulsausstoses und der exzentrischen Anomalie gegeben. Die Hamilton-Gleichungen einer Extremalen reduzieren sich dann auf eine Navigationsgleichung. Die restlichen Storungsgleichungen fur die Perihellange und die mittlere Lange der Epoche geben schlieslich den sparsamsten zeitlichen Ablauf des Raketenausstoses.
Splineapproximationen von beliebigem Defekt zur numerischen L�sung gew�hnlicher Differentialgleichungen. Teil III
1980
In the first part [5] a general procedure is presented to obtain polynomial spline approximations of arbitrary defect for the solution of the initial value problem of ordinary differential equations. The essential result is a divergence theorem in dependence of the polynomial degree and the defect of the spline functions. In this second part the convergent procedures are investigated and two convergence theorems are proved. Furthermore the question is treated, whether the convergent procedures are appropriate for the numerical solution of stiff equations. The paper is finished by a convergence theorem for a procedure producing spline approximations in a natural way by the discrete approxima…
Shooting methods for 1D steady-state free boundary problems
1993
AbstractIn this note, we present two numerical methods based on shooting methods to solve steady-state diffusion-absorption models.
Exploring chemical reactivity of complex systems with path-based coordinates: role of the distance metric.
2014
Path-based reaction coordinates constitute a valuable tool for free-energy calculations in complex processes. When a reference path is defined by means of collective variables, a nonconstant distance metric that incorporates the nonorthonormality of these variables should be taken into account. In this work, we show that, accounting for the correct metric tensor, these kind of variables can provide iso-hypersurfaces that coincide with the iso-committor surfaces and that activation free energies equal the value that would be obtained if the committor function itself were used as reaction coordinate. The advantages of the incorporation of the variable metric tensor are illustrated with the an…
Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation
1970
If, for each zero of a polynomial, an approximation is known, estimates for the errors of these approximations are given, based on the evaluation of the polynomial at these points. The procedure can be carried over to the case of multiple roots and root clusters using derivatives up to the orderk - 1, wherek is the multiplicity of the cluster.
Quark Contraction Tool - QCT
2019
We present a Mathematica package for the calculation of Wick contractions in quantum field theories — QCT. The package aims at automatically generating code for the calculation of physical matrix elements, suitable for numerical evaluation in a C++ program. To that end commonly used algebraic manipulations for the calculation of matrix elements in lattice QCD are implemented.
Descriptive Complexity, Lower Bounds and Linear Time
1999
This paper surveys two related lines of research: Logical characterizations of (non-deterministic) linear time complexity classes, and non-expressibility results concerning sublogics of existential second-order logic. Starting from Fagin’s fundamental work there has been steady progress in both fields with the effect that the weakest logics that are used in characterizations of linear time complexity classes are closely related to the strongest logics for which inexpressibility proofs for concrete problems have been obtained. The paper sketches these developments and highlights their connections as well as the obstacles that prevent us from closing the remaining gap between both kinds of lo…