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Error estimates for Galerkin finite element methods for the Camassa–Holm equation
Springer Science and Business Media LLC - Tập 142 - Trang 833-862 - 2019
We consider the Camassa–Holm (CH) equation, a nonlinear dispersive wave equation that models one-way propagation of long waves of moderately small amplitude. We discretize in space the periodic initial-value problem for CH (written in its original and in system form), using the standard Galerkin finite element method with smooth splines on a uniform mesh, and prove optimal-order
......
Stability analysis of $\theta$ -methods for neutral functional-differential equations
Springer Science and Business Media LLC - Tập 70 - Trang 473-485 - 1995
This paper deals with the subject of
numerical stability for the neutral functional-differential equation
$$
y'(t)=ay(t)+by(qt)+cy'(pt), \qquad t>0.
$$
It is proved that numerical solutions generated by
$\theta$
-methods
are convergent if
$|c|<1$
. However, our numerical experiment suggests......
On invariant closed curves for one-step methods
Springer Science and Business Media LLC - Tập 51 - Trang 103-122 - 1987
We show that a one-step method as applied to a dynamical system with a hyperbolic periodic orbit, exhibits an invariant closed curve for sufficiently small step size. This invariant curve converges to the periodic orbit with the order of the method and it inherits the stability of the periodic orbit. The dynamics of the one-step method on the invariant curve can be described by the rotation number......
Construction of basic functions for numerical utilisation of Ritz's method
Springer Science and Business Media LLC - Tập 12 - Trang 435-447 - 1968
Erratum to: Algorithms in unnormalized arithmetic. I. Recurrence relations
Springer Science and Business Media LLC - Tập 7 - Trang 354-354 - 1965
Splitting certain eigenvalue/eigenvector problems
Springer Science and Business Media LLC - Tập 8 Số 5 - Trang 412-421 - 1966
A posteriori error estimators for mixed finite element methods in linear elasticity
Springer Science and Business Media LLC - Tập 97 - Trang 757-778 - 2004
Three a posteriori error estimators for PEERS and BDMS elements in linear elasticity are presented: one residual error estimator and two estimators based on the solution of auxiliary local problems with different boundary conditions. All of them are reliable and efficient with respect to the standard norm and furthermore robust for nearly incompressible materials.
Finding all vertices of a convex polyhedron
Springer Science and Business Media LLC - Tập 12 - Trang 226-229 - 1968
The paper describes an algorithm for finding all vertices of a convex polyhedron defined by a system of linear equations and by non-negativity conditions for variables. The algorithm is described using terminology of the theory of graphs and it seems to provide a computationally effective method. An illustrative example and some experiences with computations on a computer are given.
The Chebyshev solution of certain matrix equations
Springer Science and Business Media LLC - Tập 57 - Trang 789-803 - 1990
The problem of approximating ann x m matrixC by matrices of the formX A+B Y whereA, B, X andY are of appropriate size is considered. The measure of error is the supremum of the absolute values of the individual entries in the error matrix. The problem is closely related to that of approximating a bivariate functionf by sums of functions of the formxh+gy wherex andg are functions of the first varia......
Reflections on value regions, limit regions and truncation errors for continued fractions
Springer Science and Business Media LLC - Tập 47 Số 2 - Trang 191-215 - 1985
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