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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
......
The numerical evaluation of cauchy principal values of integrals by Romberg integration
Springer Science and Business Media LLC - Tập 21 - Trang 185-192 - 1973
The problem considered is that of evaluating numerically an integral of the form
where the integrand has one or more simple poles in the interval (O,p). Modified forms of the trapezoidal and mid-ordinate rules, taking account of the singularities, are obtained; it is then shown that the resulting approximations can be extr......
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......
An error analysis for radial basis function interpolation
Springer Science and Business Media LLC - Tập 98 - Trang 675-694 - 2004
Radial basis function interpolation refers to a method of interpolation which writes the interpolant to some given data as a linear combination of the translates of a single function ϕ and a low degree polynomial. We develop an error analysis which works well when the Fourier transform of ϕ has a pole of order 2m at the origin and a zero at ∞ of order 2κ. In case 0≤m≤κ, we derive error estimates w......
Optimal addition of knots to cubature formulae for planar regions
Springer Science and Business Media LLC - - 1986
On the stability of the incomplete LU-factorizations and characterizations of H-matrices
Springer Science and Business Media LLC - Tập 69 - Trang 321-331 - 1995
Meijerink and van der Vorst [8] have
shown that the incomplete LU-factorizations are numerically stable for M-matrices. Varga, Saff and
Mehrmann [16] gave some characterizations of the H-matrices by using the
incomplete LU-factorizations of them. The purpose of this paper is to show that
the incomplete LU-factorizations of an H-matrix are at least as stable as the
complete LU-factorizations of it......
Spline qualocation methods for boundary integral equations
Springer Science and Business Media LLC - Tập 62 - Trang 295-295 - 1992
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
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