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91.
Wilhelm Niethammer 《Numerische Mathematik》1980,34(3):271-283
Summary A nonlinear generalizationÊ
z
of Euler's series transformation is compared with the (linear) Euler-Knopp transformationE
z
and a twoparametric methodE
. It is shown how to applyE
orE
, to compute the valuef(zo) of a functionf from the power series at 0 iff is holomorphic in a half plane or in the cut plane. BothE
andE
, are superior toÊ
z
. A compact recursive algorithm is given for computingE
andE
,. 相似文献
92.
Summary In this paper we consider certain structure conserving properties of finite difference methods for the solution of parabolic initial-boundary value problems. We are interested in conditions on the step size ratio =t/x
2 in one-step methods which guarantee that the number of sign changes of the discrete approximation does not increase while proceeding from one time level to the following one. This means that difference schemes of this type possess a so-called variation-diminishing property which is known to hold for continuous diffusion equations also. It turns out that our conditions on are stronger than the classical ones which imply the maximum principle for the finite difference equations. By means of an example we show that our sign stability condition is necessary too. 相似文献
93.
Harry Yserentant 《Numerische Mathematik》1980,34(2):171-187
Summary Difference methods for the numerical solution of linear partial differential equations may often be improved by using a weighted right hand side instead of the original right hand side of the differential equation. Difference formulas, for which that is possible, are called Mehrstellenformeln or Hermitian formulas. In this paper the Hermitian formulas for the approximation of Laplace's operator are characterized by a very simple condition. We prove, that in two-dimensional case for a Hermitian formula of ordern at leastn+3 discretization points are necessary. We give examples of such optimal formulas of arbitrary high-order. 相似文献
94.
Claus Schneider 《Numerische Mathematik》1980,35(1):35-43
Summary For the numerical evaluation of
, 0<<1 andx smooth, product integration rules are applied. It is known that high-order rules, e.g. Gauss-Legendre quadrature, become normal-order rules in this case. In this paper it is shown that the high order is preserved by a nonequidistant spacing. Furthermore, the leading error terms of this product integration method and numerical examples are given. 相似文献
95.
D. J. Harfiel 《Numerische Mathematik》1980,35(3):355-359
Summary LetPQ ben×n real matrices so that ifPAQ for some matrixA, thenA is nonsingular. Letp andq ben-dimensional real column vectors. This paper determines the set of all solutionsx to the equationAx=b for allA andb so thatPAQ andpbq. 相似文献
96.
Summary We consider the problem of studying the behaviour of the eigenvalues associated with spline functions with equally spaced knots. We show that they are
wherem is the order of the spline andn, the number of knots.This result is of particular interest to prove optimality properties of the Generalized Cross-Validation Method and had been conjectured by Craven and Wahba in a recent paper. 相似文献
97.
We investigate the convergence of sequences of Padé approximants for power series
相似文献
98.
Summary This paper is devoted to the numerical analysis of a bidimensional two-phase Stefan problem. We approximate the enthalpy formulation byC
0 piecewise linear finite elements in space combined with a semi-implicit scheme in time. Under some restrictions related to the finite element mesh and to the timestep, we prove positivity, stability and convergence results. Various numerial tests are presented and discussed in order to show the accuracy of our scheme.This work is supported by the Fonds National Suisse pour la Recherche Scientifique. 相似文献
99.
K. Mørken 《Constructive Approximation》1991,7(1):195-208
In this paper it is shown how the algebraic product of two spline functions, each represented in terms of B-splines, can again be represented as a linear combination of suitable B-splines. As a corollary to this result we obtain an explicit representation of a given B-spline function in terms of B-splines of some arbitrary higher degree. This generalizes some known results for raising the degree by one. Recurrence relations for both products and degree raising are established that may be useful for computation.Communicated by Larry L. Schumaker. 相似文献
100.
The left-definite Legendre type boundary problem concerns the study of a fourth-order singular differential expressionM
k
[–] in a weighted Sobolev spaceH generated by a Dirichlet inner product. The fourth-order differential equation
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