Showing papers in "Applied Numerical Mathematics in 1993"

TL;DR: The use of preconditioning methods to accelerate the convergence to a steady state for both the incompressible and compressible fluid dynamic equations and some applications for viscous flow are considered.

TL;DR: In this article, the authors consider a situation where a finite number of values which represent a sampling of weighted averages of a function ǫ corresponding to a uniform grid are given, and they introduce a reconstruction procedure R which predicts ǒx from its discrete weighted averages to any desired order of accuracy.

TL;DR: In this paper, a finite difference method for the numerical solution of partial integro-differential equations is considered and the convergence order in time is shown to be greater than one, which is confirmed by a numerical example.

TL;DR: The aim of the presented paper is to select from the large family of possible general linear methods, just a single class which has cosiderable potential for efficient implementation.

TL;DR: The convergence theory of multirate Rosenbrock-Wanner schemes is presented and automatic multirates strategies are discussed and the resulting code MROW(2)3 is tested for an inverter chain.

TL;DR: The stability characteristics of various compact fourth-and sixth-order spatial operators were used to assess the theory of Gustafsson, Kreiss and Sundstrom (G-K-S) for the semidiscrete initial boundary value problem (IBVP) as mentioned in this paper.

TL;DR: In this paper, a new stability definition for difference approximations is discussed and conditions are given that the stability of the totally discretized method follows from the stability in the semidiscrete method.

TL;DR: In this article, the authors dedicated the Jacques Louis Lions, in honor of his extraordinary contributions not only to mathematics, but also in demonstrating the crucial role that mathematics of the highest order can play throughout pure and applied science.

TL;DR: This paper will present a review of recently developed techniques in the area of parallel numerical methods for initial value problems, focusing mainly on two different approaches—parallelism across time and parallelism across space—but will also consider special techniques developed for certain classes of problems.

TL;DR: A synthesis of the various Lanczos-type algorithms for solving systems of linear equations is given, based on formal orthogonal polynomials, which enables us to avoid breakdown in Lanczo-type methods and in the CGS.

TL;DR: The construction of explicit Runge-Kutta-Nystrom methods of arbitrarily high order are described and the schemes are compared with existing (sequentiasl) high-order RKN methods from the literature and are shown to demonstrate superior behaviour.

TL;DR: In this article, the equations of incompressible fluid dynamics in three dimensions are reformulated in terms of magnetization variables; the usefulness of the resulting equations in turbulence theory and in computational fluid dynamics is explained.

TL;DR: This paper considers parallelism across time, explores a proposal made in an earlier paper [2], and reports on some tests made on that method.

TL;DR: The study of contractivity properties of Runge-Kutta methods for ODEs with respect to forcing terms with explicit methods is pursued and the regions of stability are introduced and investigated.

TL;DR: The analysis of the formulas reveals properties such as absolute stability and P-stability which indicate the ability of the method to handle highly oscillatory differential equations.

TL;DR: A very general class of waveform relaxation methods which are based on Runge-Kutta processes for the numerical solution of initial value problems for large systems of ordinary differential equations are considered.

TL;DR: In this paper, the error expansion of the iterated collocation method for nonlinear Volterra integral equations at mesh points is shown to admit an error expansion in powers of stepsize h, beginning with a term h p.

TL;DR: This paper examines a number of previously proposed methods for the parallel integration of differential equations from the perspective of computation graphs, both by direct and waveform methods.

TL;DR: This paper analyzes the convergence of extended implicit Pouzet-Volterra-Runge-Kutta methods applied to the integrodifferential-algebraic systems which arise when solving singularly perturbed integrod differentiated equations.

TL;DR: In this article, boundary value techniques based on a three-term numerical method for solving initial value problems were investigated and the notions of BV-stability and BVrelative stability were introduced in order to clarify the conditions that a 3-term scheme must satisfy for solving efficiently initial-value problems.

TL;DR: It is demonstrated that data-dependent triangulations can improve significantly the quality of approximation and that long and thin triangles, which are traditionally avoided, are sometimes necessary to have.

TL;DR: In this article, the reaction-diffusion equations are considered as an abstract Cauchy problem in an appropriate Hilbert space, assuming the space problems solved up to a prescribed tolerance.

TL;DR: Spijker as discussed by the authors reviewed various generalizations of the classical numerical range of a matrix, namely algebra numerical ranges and M-numerical ranges, and formulated three conjectures regarding stability estimates.

TL;DR: Application of these block predictor-corrector methods based on Lagrange-Gauss pairs to a few widely-used test problems reveals that the sequential costs are reduced by a factor ranging from 2 to 11 when compared with the best sequential methods.

TL;DR: The problems of accuracy and efficiency that can stand in the way of a nonsymmetric divide and conquer eigensolver based on low-rank updating are examined.

TL;DR: Estimates for the convergence of the waveform relaxation method are given for RC circuits arising as simplified models of a VLSI interconnect to suggest a new approach to WR convergence estimation.

TL;DR: Special characteristics of the PDIRK methods will be studied, such as the rate of convergence, the influence of particular predictors on the resulting stability properties, and the stiff error constants in the global error.

TL;DR: The stability properties of three particular BVMs when used for solving linear systems of ODEs and an efficient implementation of these methods are described.

TL;DR: For this is no search for earthly things but a seeking out of the mysteries and hidden sweets of our Lord, and the divine secrets which the most high Master will disclose to that blessed knight whom He has chosen for his seruant from amongst the ranks of chivalry as discussed by the authors.

TL;DR: In this paper, it was proved that in exact arithmetic row exchanges are not necessary and the same result holds for sufficiently high precision arithmetic in Gauss elimination and also for a class of totally positive matrices (which included B-spline collocation matrices), in Neville elimination.