Showing papers in "Journal of Computational and Applied Mathematics in 1999"

TL;DR: In this paper, the authors introduce the class of k-uniformly convex functions k-UCV, with the property that the values of the expression 1+zf″(z)/f′(z) lie inside the domain Ω k.

TL;DR: In this article, numerical methods and algorithms for the solution of NLTE stellar atmosphere problems involving expanding atmospheres, e.g., found in novae, supernovae and stellar winds, are discussed.

TL;DR: In this article, a new implementation of the Radau IIA method with a variable order strategy is described. But the authors do not discuss the theoretical properties of the new algorithm.

TL;DR: In this article, the authors presented finite-difference solution and analytical solution of the finitedifference approximations based on the standard explicit method to the one-dimensional Burgers equation which arises frequently in the mathematical modelling used to solve problems in fluid dynamics.

TL;DR: In this paper, a general expression is derived for a three-term Strang splitting in the pure initial value case, for a class of advection-diffusion-reaction problems the splitting error is analyzed in greater detail.

TL;DR: In this paper, the authors present a compilation of all the so-called monomial cubature rules which have appeared since the publication of Stroud's work, for most of the regions contained there plus some cubatures which appeared earlier but were not included in [98] for some reason.

TL;DR: In this article, a special high-accuracy direct force summation N-body algorithms and their relevance for the simulation of the dynamical evolution of star clusters and other gravitating n-body systems in astrophysics are presented, explained and compared with other methods.

TL;DR: In this paper, the authors describe a methodology for numerical solution of 3D self-gravitational hydrodynamics problems with unprecendented resolution, and present illustrative applications for both isothermal and nonisothermal cloud collapse.

TL;DR: In this paper, a review on the two principle methods used to evolve nuclear abundances within astrophysical simulations, evolution via rate equations and via equilibria, is presented, focusing on efficient solution of these matrix equations, by making best use of the sparseness of these matrices.

TL;DR: In this article, a method based on convex combinations for morphing corresponding pairs of tilings in R 2 was described, which always yields a valid morph when the boundary polygons are identical, unlike the standard linear morph.

TL;DR: In this article, it was shown that the Laguerre polynomials are eigenfunctions of a (finite order) differential operator, and that they can be replaced by functions.

TL;DR: In this article, a Taylor-series expansion method is presented for a class of Fredholm integral equations of the second kind with smooth and weakly singular kernels, which can be expressed explicitly in a simple, closed form.

TL;DR: It is demonstrated that by using nonstandard schemes, all the difficulties found by Chen and Solis can be eliminated, and that qualitatively correct numerical solutions are obtained for all values of the step size.

TL;DR: In this paper, a two-dimensional tree-code plus a multipole expansion is proposed for the determination of the deflection angle of a single lens in a cosmological lens simulation.

TL;DR: In this article, the unconditional stability of the θ-method for the heat equation with nonlocal boundary conditions is proved for θ⩾ 1 2, subject to a condition that is much weaker than the one assumed in a paper by Ekolin.

TL;DR: In this article, the authors introduce the classical stellar atmosphere problem and describe its numerical solution, which consists of the solution of the radiation transfer equations under the constraints of hydrostatic, radiative and statistical equilibrium (non-LTE).

TL;DR: In this paper, a double exponential transformation is presented to obtain a quadrature formula for Fourier-type integrals, where f(x) is a slowly decaying analytic function on (0,∞).

TL;DR: In this article, the extended Clenshaw-Curtis method for finite Fourier integrals is discussed, and a number of timed comparisons are made between the various implementations which appear in the literature.

TL;DR: In this article, the authors compare the finite Fourier (-exponential) and Fourier-Kravchuk transform, which is a canonical transform whose fractionalization is well defined.

TL;DR: In this article, Zhang et al. considered the problem of adjusting the cost coefficients of a given LP problem as less as possible so that a known feasible solution becomes the optimal one.

TL;DR: In this article, the authors analyze two explicit methods for the solution of an inverse heat conduction problem and confront them with the least-squares method, using for the problem a classical finite difference method and a method based on an integral formulation.

TL;DR: The underlying theory for an algorithm that computes the Voronoi diagram and medial axis of a planar domain bounded by free-form (polynomial or rational) curve segments is presented and unambiguous characterizations for edges in both these categories are given.

TL;DR: In this paper, a variational formulation of the adiabatic eigenvalue problem for a star's internal structure and dynamics of the Sun can be inferred from observed frequencies of solar oscillations and acoustic travel times.

TL;DR: In this article, the authors compare multigroup flux-limited diffusion and Boltzmann transport in post-core bounce supernova environments, with an eye toward the quantities central to the neutrino-heating, shock-revival mechanism.

TL;DR: In this paper, the authors deal with the problem of constructing efficient rules for the numerical evaluation of integrals of functions which are very smooth everywhere in the domain of integration, except at the boundaries where they possess mild singularities.

TL;DR: In this paper, a comparison of the three types of approximations is given with an ideal digital differentiator by comparing their frequency responses, which reveals that the central difference approximation can be used as digital differentiators, because they do not introduce any phase distortion and their amplitude response is closer to that of an ideal differentiator.

TL;DR: In this paper, an upwind finite difference scheme on a modification of Shishkin's piecewise uniform mesh for a model singularly perturbed convection-diffusion problem in two dimensions is considered.

TL;DR: In this article, the stability properties of a P-stable multistep algorithm with an order greater than two were studied, and it was shown that this algorithm is conditionally P-stable with θmax = 3.4.

TL;DR: In this article, an explicit formulae and recurrence relations for the calculation of generalized B-splines of arbitrary order are given, and main properties of GB-spline and their series are derived.

TL;DR: In this paper, the authors present spectral methods developed in their group to solve three-dimensional partial differential equations arising from astrophysical problems in the framework of general relativity, where the emphasis is laid on equations arising in the universe.