Showing papers in "Applied Numerical Mathematics in 2006"

TL;DR: In this paper, a fully discrete difference scheme is derived for a diffusion-wave system by introducing two new variables to transform the original equation into a low order system of equations. And the solvability, stability and L∞ convergence are proved by the energy method.

TL;DR: In this paper, the authors examined some practical numerical methods to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain, and the stability, consistency, and (therefore) convergence of the methods are discussed.

TL;DR: An overview of some of the mathematical models appearing in the literature for use in the glucose-insulin regulatory system in relation to diabetes is given, enhanced with a survey on available software.

TL;DR: It is found the new approach can successfully restore the particle consistency and can therefore significantly improve the approximation accuracy.

TL;DR: In this paper, a one-parameter family of explicit fourth-order methods for oscillatory systems of the form y" + Ky = f (t, y), K being a symmetric positive semi-definite matrix, is obtained.

TL;DR: This paper proposes to discretize derivative operators by pseudospectral techniques and turn the original eigenvalue problem into a matrix eigen value problem, which is shown to be particularly efficient due to the well-known "spectral accuracy" convergence of pseudOSpectral methods.

TL;DR: In this paper, a family of numerical integrators based on the Magnus series expansions is presented for solving non-linear ODEs with no commutators, which can be tailored to preserve geometric properties of the solutions.

TL;DR: A space-time discontinuous Galerkin (DG) finite element discretization of the advection-diffusion equation on time-dependent domains results in an efficient numerical technique for physical applications which require moving and deforming elements, is suitable for hp-adaptation and results in a fully conservative discretizations.

TL;DR: The performance of the preconditioner for Helmholtz problems at high wavenumbers in heterogeneous media is evaluated and different methods for the approximation of the inverse of a complex-valued Helmholz operator are discussed.

TL;DR: It is proved that the new method for the numerical computation of characteristic roots for linear autonomous systems of Delay Differential Equations (DDEs) converges with the same order as the underlying RK scheme and is compared with other existing techniques.

TL;DR: In this article, the authors investigated Chebyshev spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations and proved the superlinear convergence of the iterations.

TL;DR: Based on the multi-symplecticity of the Schrodinger equations with variable coefficients, this paper gave a multisymplectic numerical scheme, and investigated some conservative properties and error estimation of it.

TL;DR: Three different approaches to step size selection are presented and discussed: control theory, signal processing, and adaptivity, in the sense that the time step should be covariant or contravariant with some prescribed function of the dynamical system's solution.

TL;DR: This paper proposes and compares two finite element implementations that cure this ill-behaviour in free-surface fluid dynamics problems without the need to resort to combined strategies (such as e.g. particle level set).

TL;DR: In this paper, a second order monotone numerical method is constructed for a singularly perturbed ordinary differential equation with two small parameters affecting the convection and diffusion terms, and an asymptotic error bound in the maximum norm is established theoretically whose error constants are shown to be independent of both singular perturbation parameters.

TL;DR: In this paper, the authors present in a general framework the hybrid discretization of unilateral contact and friction conditions in elastostatics, and an existence and uniqueness result for the solutions to the discretized problem is given in the general framework.

TL;DR: In the course of developing a completely new user interface, the authors have added significantly to the capabilities of DKLAG6, a FORTRAN 77 code widely used to solve delay differential equations.

TL;DR: A second-order TVD (TVD for the scalar case) extension is presented and numerical results for the two-dimensional Euler equations on non-Cartesian geometries are shown and the Godunov scheme is seen as the best of all first-order monote schemes.

TL;DR: In this paper, a finite-volume method is developed to simulate the dynamics of peakons, which is adaptive, high resolution and stable without any explicit introduction of artificial viscosity.

TL;DR: In this article, a numerical method based on an integro-differential equation and local interpolating functions is proposed for solving the one-dimensional wave equation subject to a non-local conservation condition and suitably prescribed initial-boundary conditions.

TL;DR: This work considers the numerical approximation of a model convection-diffusion equation by standard bilinear finite elements and proves optimal order error estimates in the e-weighted H1-norm valid uniformly, up to a logarithmic factor, in the singular perturbation parameter.

TL;DR: Fractional order partial differential equations are generalizations of classical PDEs and are used in many applications such as fluid flow, finance and computer vision as discussed by the authors, where fractional order PDE models are used for simulation.

TL;DR: In this paper, the singularity formation for the Camassa-Holm equation and for Prandtl's equations was studied using spectral methods, and the authors tracked the singularities in the complex plane estimating the rate of decay of the Fourier spectrum.

TL;DR: A second order shape calculus enables us to analyze the shape problem under consideration and to prove convergence of a Ritz–Galerkin approximation of the shape.

TL;DR: Finite difference methods for a two-dimensional quasi-static Biot's consolidation problem are considered in this article, where a priori estimates for displacements and pressure in discrete energy norms are obtained and corresponding convergence results are proved.

TL;DR: This work exploits the special properties of the models that arise in the control theory application to solve difficult problems with enough accuracy and enough speed for design purposes.

TL;DR: In this paper, it was shown that the solutions of delay differential and implicit and explicit neutral delay differential equations (NDDEs) may have discontinuous derivatives, but it has not been appreciated (sufficiently) that the solution of NDDEs and, therefore, solutions of Delay Differential Algebraic Equations (DDE) need not be continuous.

TL;DR: This work compares piecewise linear and polynomial collocation approaches for the numerical solution of a Fredholm integro-differential equations modelling neural networks.

TL;DR: In this article, the viscous quantum hydrodynamic equations for semiconductors with constant temperature were numerically studied, and two different numerical techniques were used: a hyperbolic relaxation scheme and a central finite-difference method.

TL;DR: The Ultra-Bee scheme is investigated, particularly interesting here for its anti-diffusive property in the transport of discontinuous functions.