1,721,027 research outputs found
End conditions for improved cubic spline derivative approximations
No full textAbstractWe consider the problem of deriving accurate end conditions for cubic spline interpolation at equally spaced knots. In particular we derive a number of end conditions which lead to derivative approximations of high accuracy
Pole type singularities and the numerical conformal mapping of doubly-connected domains
No full textLet f be the function which maps conformally a given doubly-connected domain onto a circular annulus, and let Ω
H(z) = f '(z) / f(z) - 1/z .
In this paper we consider the problem of determining the main singularities of the function H in compl)(Ω∂∪Ω. Our purpose is to provide information regarding the location and nature of such singularities, and to explain how this information can be used to improve the efficiency of certain expansion methods for numerical conformal mapping
Stability and covergence properties of Bergman Kernel methods for numerical conformal mapping
No full textIn this paper we study the stability and convergence properties of Bergman kernel methods, for the numerical conform al mapping of simply and doubly- connected domains. In particular, by using certain well-known results of Carleman, we establish a characterization of the level of instability in the methods, in terms of the geometry of the domain under consideration. We also explain how certain known convergence results can provide some theoretical justification of the observed improvement in accuracy which is achieved by the methods, when the basis set used contains functions that reflect the main singular behaviour of the conformal map
Superconvergence properties of quintic interpolatroy splines
No full textLet Q be a quintic spline with equi-spaced knots on [a,b] interpolating a given function y at the knots. The parameters which determine Q are used to construct a piecewise defined polynomial P of degree six. It is shown that P can be used to give at any point of [a,b] better orders of approximation to y and its derivatives than those obtained from Q. It is also shown that the superconvergence properties of the derivatives of Q, at specific points of [a,b], are all simple consequences of the properties of P
A class of C2 piecewise quintic polynomials
No full textA new class of C2 piecewise quintic interpolatory polynomials is defined. It is shown that this new class contains a number of interpolatory functions which present practical advantages, when compared with the conventional cubic spline
On the comparison of two numerical methods for conformal mapping
No full textLet G be a simply-connected domain in the t—plane (t = x + iy), bounded by the three straight lines x = 0, y = 0, x =1 and a Jordan arc with cartesian equation y = τ (X). Also, let g be the function which maps conformally a rectangle R onto G, so that the four corners of R are mapped onto those of G. In this paper we show that the method con-sidered recently by Challis and Burley [2], for determining approx- imations to g, is equivalent to a special case of the well-known method of Garrick [8] for the mapping of doubly-connected domains, Hence, by using results already available in the literature, we provide some theoretical justification for the method of [2]
A posteriori corrections for cubic and quintic interpolating splines at equally-spaced knots
No full textThe method proposed recently by Lucas [13], for the a posteriori correction of odd degree interpolating periodic splines is extended to non-periodic cubic and quintic splines
An orthonormalization method for the approximate conformal mapping of multiply-connected domains
No full textWe consider the use of an orthonormalization method for constructing approximations to one of the standard conformal maps for multiply-connected domains. The method has been used successfully in [12], but only for the mapping of doubly-connected domains. Our purpose here is to consider its application to the mapping of domains whose connectivity is greater than two
The determination of the poles of the mapping function and their use in numerical conformal mapping
No full textLet f be the function which maps conformally a simply-connected domain Ω onto the unit disc. This paper is concerned with the problem of determining the dominant poles of f in comp1(Ω∩∂Ω), and of using this information in order to obtain accurate numerical approximations to f by means of the Bergman kernel method
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