Showing papers in "Journal of Computational and Applied Mathematics in 1985"

TL;DR: In this paper, a technique for reducing their index from three to two is introduced and it is shown that variable-order, variable-step BDF methods converge for these index two problems.

TL;DR: The discretized Stieltjes procedure as discussed by the authors is one of the most widely used methods for generating orthogonal polynomials on the semicircle and can be used to solve some special problems in approximation theory and in the summation of slowly convergent series.

TL;DR: This paper surveys some of these results and presents new results showing how much more efficient and robust block matrix incomplete factorization preconditioning methods can be as compared to other, admittingly also efficient, methods.

TL;DR: A survey of the results known to date about quadrature formulas obtained by variable transformation followed by an application of the trapezoidal rule with an equal mesh size focuses on an asymptotically optimal formula called the double exponential formula, abbreviated as the DE-rule, which is characterized by thedouble exponential decrease of its weights in the neighborhood of the end points of the transformed interval of integration.

TL;DR: In this paper, the Hermite problem Hk(A, V) is solved in V = Pkn(D, τ) iff n ⩾ 4k+1 (Ženisek).

TL;DR: The ability of a recent formulation of the Tau method of Ortiz and Samara to give approximate solutions of a high accuracy of linear PDEs with variable coefficients is used to produce numerical solutions of nonlinear partial differential equations as mentioned in this paper.

TL;DR: A review of the most significant results obtained the past ten years on convergence acceleration methods, divided into four sections dealing respectively with the theory of sequence transformations, the algorithms for such transformations, their implementation and their applications to various subjects of numerical analysis.

TL;DR: In this paper, a mathematical model, consisting of a system of partial differential equations, has been developed at the Danish Agency of Environmental Protection for studying the long-range transport of sulphur pollutants in the atmosphere.

TL;DR: In this article, the existence of bivariate spline, the dimension and basis of the bivariate Spline spaces S μ k (Δ) with various partitions Δ, and some results on higher dimensional splines are presented.

TL;DR: An algorithm for the computation of a Hopf bifurcation point based on a direct method, i.e. an augmented time independent system is solved and the bandstructure of the Jacobian matrix is exploited.

TL;DR: In this article, the theory of recursive generation of systems of orthogonal polynomials is described and illustrated by means of a typical example of practical application, which is applied to the polynomial of Legendre.

TL;DR: In this article, the size of the operator C (A) where A is a linear operator in a Hilbert space with norm at most 1 was studied and an application to variable step integration of initial value problems using one-leg methods was given.

TL;DR: In this article, a unified derivation of the upper and lower bounds of the errors in Newton's process, obtained by Dennis [4], Tapia [27], Gragg-Tapia [6] and recently by Potra-Ptak [20] and Miel [15], with the use of different techniques is given.

TL;DR: In this paper, a new family of two-step fourth-order methods which are superstable for the test equation is presented, including a modification of the trapezoidal method which results in a superstable method.

TL;DR: The van der Corput sequence and other low discrepancy sequences can be seen as orbits of ergodic measure preserving transformations constructed on the unit interval by splitting and stacking techniques.

TL;DR: Using these options to characterize the various procedures which have been proposed, the recent research on Lanczos methods for solving real symmetric eigenvalue problems is briefly surveyed.

TL;DR: Various heuristics to obtain computable error estimates are compared by calculating their performance profiles on the Lyness family of integrands to find the best heuristic based on Gaussian quadrature.

TL;DR: In this paper, some new continued fractions for incomplete gamma functions γ(a, z ) and Γ( a, z ), with a and z complex, are derived, which can be evaluated by a numerically stable backward recurrence algorithm.

TL;DR: Results of preliminary computer tests on ‘difficult’ renumbering problems are presented, and algorithms proposed by Arany and several other new algorithms are described, and RLSF width, bandwidth, profile, and CPU time are compared for four algorithms.

TL;DR: In this article, singular value decomposition (SVD) is used to derive linear algebraic equations which are derived for numerical solution of first kind Fredholm integral equations arising in two-dimensional potential theory.

TL;DR: It is investigated whether certain structural properties of a traffic network can be identified by an analysis of the spectrum of its adjacency matrix by analysing the values of the RSPs in the matrix.

TL;DR: In this paper, the authors studied the weak limit of this sequence of measures and gave some results on the rate of this asymptotic behaviour, in particular the results show how the behaviour of the spectral measure, with respect to which the polynomials are orthogonal, affects this asyptotic zero behaviour.

TL;DR: In this article, the authors considered the numerical solution of second kind Fredholm integral equations in one dimension by using the collocation method and its iterated variant, and they gave a corresponding superconvergence result for the iterated collocation solution when continuous piecewise polynomials with no continuity requirements on the derivatives are used.

TL;DR: Bounds for the error order and error constant of full- and semidiscretizations of hyperbolic problems are given and lower bounds for these scaled error constants are given using the order star technique.

TL;DR: In this paper, a numerical method is described for the conformal mapping of simply connected domains whose boundaries contains sharp corner points. The method is based on a first kind integral equation formulation due to Wendland [15].

TL;DR: In this paper, the results of the solution of the homogeneous Navier-Stokes equations in the halfplane for the slow motion of viscous incompressible fluids were generalized to the class of the micropolar fluids for the case of the given shear stresses on the boundary.

TL;DR: In this paper, a boundary element method is developed to solve the steady convective diffusion equation in n dimensions, where the transformation into the selfadjoint or symmetric operator is used under a certain assumption, and a boundary integral equation is derived from the Green's second identity.

TL;DR: In this article, the Stieltjes integral is exploited for summation of Fourier series by numerical integration, where the coefficients of the series are given analytically, and then the numerator of the integrand is determined by the aid of the inverse of the two-sided Laplace transform, while the denominator is standard for all power series.