Showing papers in "Journal of Computational and Applied Mathematics in 1981"

TL;DR: In this article, the criteria to be satisfied by embedded Runge-Kutta pairs of formulae are reviewed, together with tests on their efficiency relative to other high-order forms in current use.

TL;DR: In this article, an extension of the influence curve to non-Fisher-consistent functionals is proposed in order to investigate the infinitesimal robustness of more general statistics, e.g. those used in hypothesis testing.

TL;DR: In this article, the Fourier transform of B-spline moments with arbitrary knots has been studied and a simple connection between the moments of such splines and the extended Stirling numbers of the second kind has been made.

TL;DR: In this article, a unified method for obtaining the Pade approximants for some hypergeometric functions is given, based on a set of linear equations that are obtained from the determinant expressions for Pade approximation and their solution by using two simple theorems developed in the text.

TL;DR: In this paper, a cubic spline method is described for the numerical solution of a two-point boundary value problem involving a fourth order linear differential equation, which is closely related to a known fourth order finite difference scheme.

TL;DR: For the confluent hypergeometric functions U (a, b, z, z) and M(a,b, z), asymptotic expansions are given for a → ∞ as discussed by the authors.

TL;DR: In this article, a globally convergent homotopy algorithm is applied to the boundary value problem, and numerical results for a wide range of parameter values are reported for a variety of problems.

TL;DR: Dehesa et al. as discussed by the authors presented a survey of methods to determine the collective properties of the spectrum of a large-scale many-body system, including the spectral distribution of an arbitrary starting vector 11~> of the reduced Hilbert space.

TL;DR: In this paper, a finite element method for computing numerical approximations of the solution of the second order singularly perturbed two-point boundary value problem on [− 1, 1] ϵ u″ + pu′ = f, u(− 1) = u(1) = 0, 0 d dx ) is described.

TL;DR: In this article, a new method for solving non-linear parabolic partial differential equations, based on the method of lines, is developed, and the method has been tested on a number of difficult problems in the literature and has proved to be most successful.

TL;DR: In this article, the authors dealt with non-linear Volterra integral equations of the type y = f(x) + ǫ 0x H[t, x, y (t), y (x)] dt.

TL;DR: In this article, the authors propose a method for continuing an analytic function from its power series expansion that enables us to choose the location of cuts joining the branch points, which is superior to the Pade approximant method.

TL;DR: A new algorithm for the rational Hermite interpolation table is described that reduces to the qd algorithm of Rutishauser in the Pade case and shares several properties with Rutisha user's algorithm.

TL;DR: In this paper, the Wiener process with constant drift is modified by a time-dependent retaining barrier that increases at a constant rate and by an absorbing barrier at zero, and explicit expressions in terms of series expansions are derived for the Laplace transform and the probability density function of the time of absorption.

TL;DR: In this article, a composite expansion solution to the Troesch problem using the method of matched asymptotic expansions is presented. But their solution is uniformly valid for all n>0 and y⩾0.

TL;DR: In this paper, the problem of deriving accurate end conditions for cubic spline interpolation at equally spaced knots was considered and a number of end conditions which lead to derivative approximations of high accuracy was derived.

TL;DR: The quadrature formula is obtained by using a trapezoidal rule after a non-linear transformation, and allows to deal with integrand singularities on the surface or in the centre of the sphere.

TL;DR: In this paper, a bibliography lists about four hundred references to published papers, theses, and books which deal with non-differentiable optimization problems or contribute to the field of non-convex non-smooth analysis useful for the study of such optimization problems.

TL;DR: In this article, the Gauss-Legendre quadrature rule is used to numerically integrate an analytic function and the error in a standard approximation to the kernel function is investigated for this purpose.

TL;DR: In this paper, the separable integer programming problem with nested constraints is shown to be equivalent to its continual version obtained by piecewise linear continuation of the cost functions, and a new approach to solution of the latter based on its successive reduction in size is suggested.

TL;DR: In this article, the applicability of the restrictive conditions of linear stability as well as the effect of an additional boundary condition on the otherwise well-posed Cauchy problem are investigated. But their results are limited to finite-difference representations of the convection-diffusion equation.

TL;DR: This paper constitutes a computer program for the discrete linear restricted Chebyshev approximation problem that is written in ANSI basic FORTRAN language and may be calculated as special cases by this program.

TL;DR: In this paper, a necessary condition on the first correction is developed which avoids the expense of solving the algebraic equations only to reject the step, which provides early prediction of all modes of failure to take a step with an implicit formula.

TL;DR: In this paper, it was shown that a super-diagonal ray sequence of Pade approximants of a Stieltjes series with finite radius of convergence is a pierced-heart region in the complex plane.

TL;DR: In this article, a computer approach to atomic and molecular dynamics is developed which utilizes known experimental values of ionization energies, and applications are made to the hydrogen atom, the hydrogen ion, and the hydrogen molecule.

TL;DR: In this paper, a simple model of the molecular dynamics of O2 is developed for interactions which are not readily amenable to quantum mechanical analysis, including electron-electron interactions.

TL;DR: An algorithm for empirically calculating the expected number of optimal and near-optimal solutions in a random Euclidean travelling salesman problem based on well known geometric properties of the optimal tour is presented.

TL;DR: In this article, a continuation method was developed to solve the nonlinear eigenvalue problem describing the unsteady, squeezing flow of a viscous fluid between elliptic plates, which is conceptually simple, noniterative, insensitive to the first approximation and works for all values of squeeze number S characterizing the flow.