Showing papers in "Applied Numerical Mathematics in 2007"

TL;DR: In this paper, a new method for obtaining validated solutions of initial value problems for ODEs with interval-valued parameters is presented, and the method also accounts for intervalvalued initial values.

TL;DR: In this paper, the authors describe methods for estimating diagonals and traces of matrices in these situations, using random test vectors and special vectors obtained from Hadamard matrices.

TL;DR: In this article, alternating direction implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection-diffusion equations with cross derivative terms were studied.

TL;DR: Two schemes based on discontinuous Galerkin methods for modeling fully implicit formulations of two-phase flow problems arising in porous media do not require slope limiting or upwind stabilization techniques.

TL;DR: Global convergence properties of the proposed methods are established and numerical results are provided, showing that the new method, called the Newton-GMRES with quasi-conjugate-gradient backtracking (NGQCGB), is very robust and effective.

TL;DR: The spectral properties and the computational performance of a positive stable block triangular preconditioner for the solution of the general symmetric saddle point problem and the eigenvalues of the preconditionsed matrix are shown to be real.

TL;DR: It is shown uniform decrease in energy error for an hp-adaptive algorithm with automatic hp selection on the elliptic model boundary value problem and it is demonstrated that the algorithm achieves the known theoretical optimal error behavior.

TL;DR: In this article, numerical methods for solving integro-differential equations which generalize the well-known Fisher equation were studied. And the stability and convergence of the methods are studied.

TL;DR: In this article, a new fourth-order implicit time-stepping scheme for the numerical solution of the acoustic wave equation, as a variant of the conventional modified equation method, was proposed.

TL;DR: In this article, a numerical study of the Gibbs phenomenon with multiquadric radial basis functions for discontinuous functions is presented, which is characterized by two parameters: the shape parameter and the magnitude of the jump discontinuity.

TL;DR: The orthogonal approximation is developed by using generalized Laguerre functions to form a spectral method for a partial differential equation of degenerate type, which plays an important role in financial mathematics and other fields.

TL;DR: In this article, a unified analysis of implicit and explicit error estimators for a general class of locally conservative methods applied to nonlinear elliptic problems is presented, based on a proper decomposition of the error itself.

TL;DR: This technique is a combination of a low rank update spectral preconditioner and a Krylov solver that computes on the fly approximations of the eigenvectors associated with the smallest eigenvalues.

TL;DR: A flux-based method of characteristics for the advective part and a semi-implicit treatment of diffusive part removes the standard CFL condition on time step and it decreases CPU times significantly.

TL;DR: In this article, a spectral Petrov-Galerkin method for the linear and nonlinear stability analysis of the pipe or Hagen-Poiseuille flow is presented. But the method is unusual in being based on Chebyshev polynomials of selected parity for the radial variable, avoiding clustering of the quadrature points near the origin, satisfying appropriate regularity conditions at the pole and allowing the use of a fast cosine transform if required.

TL;DR: In this paper, the authors present a mathematical framework for biochemical problems, which includes an exact definition of biochemical conservation: elements and energy, rather than state variable units, are conserved.

TL;DR: In this article, the authors investigated the lowest-order Raviart-Thomas mixed finite element method for second-order elliptic problems posed over a system of intersecting two-dimensional polygons placed in three-dimensional Euclidean space.

TL;DR: An efficient algorithm for the approximation of functions and their derivatives using radial basis functions (RBFs) is proposed, capable of solving large-scale problems with more than 100@?000 interpolation points in two dimensions.

TL;DR: In this article, a three-level second-order implicit algorithm is proposed to solve viscous and non-viscous wave equations without introducing auxiliary variables, and a locally one-dimensional (LOD) procedure is suggested to solve problems of diagonal diffusion tensors in cubic domains efficiently.

TL;DR: A new embedded pair of explicit RKN methods adapted to the numerical integration of general perturbed oscillators is derived and can be used to deal with the particular problems in which the perturbed functions are independent of y^' but the general problems.

TL;DR: In this article, a tractable way of seeking weak order conditions of a stochastic Runge-Kutta family for differential equations with a multi-dimensional Wiener process is given.

TL;DR: In this paper, a new semilocal convergence result of Newton-Kantorovich type for the Halley method is presented, where a new technique is provided to analyze the semileocal convergence.

TL;DR: In this article, a Legendre spectral method for first-order hyperbolic equations with periodic boundary conditions is presented, and convergence analysis of the spectral scheme is given and the L2-optimal error estimate in spatial is achieved.

TL;DR: In this article, a nodal high-order spectral finite volume method is developed for the cubed-sphere and a third-order explicit strong stability preserving scheme is employed for the time integration.

TL;DR: In this article, a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives, from which the linear convergence of the algorithm is deduced.

TL;DR: It is demonstrated that direct transcription methods, which use a different approach, can successfully solve some higher index equality constrained optimal control problems and that the role of the index needs reinterpretation when usingdirect transcription methods.

TL;DR: In this paper, Gautschi's exponentially fitted Stormer/Verlet method is discussed and its various interpretations are given, and the problem of choosing the optimal frequency for such exponentially fitted methods is discussed.

TL;DR: In this paper, the authors present the solution of a very important problem, which can be used for active noise shielding and vibration control, which is related with shielding one domain from the influence of another one via a distribution of additional sources outside of the first domain.

TL;DR: In this paper, the Kepler equation for the parameters of an elliptical orbit, E-e sin(E) = M, is reduced from a transcendental to a polynomial equation by expanding the sine as a series of Chebyshev polynomials.

TL;DR: In this article, the wave equation with unilateral constraints is considered and the authors consider the transverse motion of a vibrating string with fixed ends impacting a stationary rigid obstacle and prove the convergence of the numerical trajectories in both semi-discrete case and fully-decrete case.