Showing papers in "Applied Numerical Mathematics in 1995"

TL;DR: In this paper, the authors examined the Chebyshev tau method for a variety of eigenvalue problems arising in hydrodynamic stability studies, particularly those of Orr-Sommerfeld type.

TL;DR: This paper investigates two ways of improvement for the reduction of communication overhead introduced by inner products in the iterative solution methods CG and GMRES( m).

TL;DR: This paper describes FORTRAN-77 implementations of simplified versions of the look-ahead Lanczos algorithm and of the quasiminimal residual (QMR) method, which is a Lanczos-based iterative procedure for the solution of linear systems.

TL;DR: In this article, a numerical approximation of the nonlinear diffusion problem appearing in image processing is discussed, based on Rothe's approximation in time and on the finite element approach in space.

TL;DR: QR-based method for computing the first few Lyapunov exponents of continuous and discrete dynamical systems and algorithmic developments are discussed.

TL;DR: In this paper, three explicit methods are discussed and compared for a selected chemical kinetics system which is representative for the state-of-the-art: explicit QSSA type, two-step backward differentiation and Gauss-Seidel iteration.

TL;DR: For problems with periodic solution and for integrable systems, the error growth is only linear for symplectic and symmetric methods, compared to a quadratic error growth in the general case as mentioned in this paper.

TL;DR: In this paper, the conditions sufficient to ensure positivity and linearity preservation for a cell-centered finite volume scheme for time-dependent hyperbolic equations using irregular one-dimensional and triangular two-dimensional meshes are derived.

TL;DR: In this article, proper ways to combine numerical schemes for advective transport and nonlinear chemistry are considered, and the results are obtained with splitting in a so-called fractional step approach.

TL;DR: An adaptive Rothe method for two-dimensional problems combining an embedded Runge-Kutta scheme in time and a multi-level finite element discretization in space is presented.

TL;DR: It is shown that many of these linear multistep methods can also be conveniently used to approximate with high accuracy continuous BVPs.

TL;DR: Two well-known deterministic strategies that extend the Arnoldi process from the first stage are discussed and a new one that performs Krylov steps adaptively to minimize the residual of the next approximation is presented.

TL;DR: A technique to develop efficient schemes for three-stage methods for implicit Runge-Kutta methods is proposed and particular schemes are constructed for the case of Gauss and RadauII A methods.

TL;DR: In this paper, the best numerical schemes are those which use higher order finite difference approximations for the derivatives (but not vast templates), perform interpolation directly over the derivative (and not the function), and have an odd power as the leading term in the polynomial expansion for the derivative.

TL;DR: A convergence result for minimization problems by discretizing this equation via fixed time-stepping one-step methods is derived and it is shown that for a certain class of one- step methods the totality of the discrete and the continuous ω-limit sets coincide if the stepsize is sufficiently small.

TL;DR: In this paper, a linearization of non-linear index-2 systems is considered and the standard Implicit Function Theorem is applied to apply the standard implicit function theorem again, and the local convergence of the Newton-Kantorovich method (quasilinearization) result immediately.

TL;DR: Weighted least-squares forms of the underlying equation are added to the basic Galerkin finite element semidiscretization in order to accomodate the method to (possibly locally varying) convective, reactive or diffusive terms.

TL;DR: In this article, the accuracy of the iteration coefficients of BiCG depends on the particular choice of the hybrid method and how this affects the speed of convergence, and look-ahead strategies for the determination of appropriate values for l in BiCGstab( l ).

TL;DR: In this article, the long-time behavior of a discretised evolution equation is studied and the existence and stability of the basic steady states are systematically studied, as functions of the grid spacings and problem parameters.

TL;DR: In this article, the authors derive boundary value methods based on k-step Adams-type methods for the solution of initial value problems and prove that the choice of boundary conditions, instead of the usual initial conditions, improves the stability properties of the classical Adams methods.

TL;DR: An algorithm by which the discrete numerical solution of a Volterra integral equation obtained from a classical Newton-Cotes-type approximation of its integral part is corrected in an iterative way and turns out to be parallelizable.

TL;DR: Adaptive integrated space-time hp-refinement algorithms for one-dimensional vector systems of parabolic partial differential equations with new techniques simplify spatial error estimation with high-order approximation; integrate spatial and temporal discretization and enrichment; and enable the selection of future meshes and acceptance of partial time steps.

TL;DR: It is shown that as a preconditioner, multistep red-black SOR can give good scaled speedup and there has been some confusion in the literature as to whether this approach should be effective.

TL;DR: This paper investigates the convergence of continuous time and discrete time iteration processes that are obtained from Runge-Kutta methods, and derives convergence results that are relevant in applications to nonlinear, nonautonomous, stiff initial value problems.

TL;DR: Computational schemes for various types of one- and two-dimensional invariant manifold are considered and emphasis is on the choice of parametrisation for the manifold and how this leads to different algorithms.

TL;DR: In this article, the convergence results of implicit Runge-Kutta methods when applied to differential-algebraic equations of index 3 in Hessenberg form are shown. But they are not shown in terms of global superconvergence.

TL;DR: In this paper, the authors show that the full nonstiff order of temporal convergence is attained in the interior of the domain, even in the case of incompatible initial-boundary data or nonsmooth boundaries.

TL;DR: In this paper, an algorithm to numerically invert two-dimensional Laplace transforms is presented, which is an extension of the one-dimensional methods based on the representation of the inverse function in terms of Fourier series.

TL;DR: The schemes are completely analysed: consistency, stability, existence and convergence are established and some numerical experiments are reported in order to show numerically the results proved.

TL;DR: Recent results on residual smoothing are reviewed and it is observed that certain of these are equivalent to results obtained by different means that relate “peaks” and “plateaus” in residual norm sequences produced by certain pairs of Krylov subspace methods.