A software package for the numerical integration of ODEs by means of high-order Taylor methods.
A solution of the continuous Lyapunov equation by means of power series
A Solver for Complex-Valued Parametric Linear Systems
This work reports on a new software for solving linear systems involving affine-linear dependencies between complex-valued interval parameters. We discuss the implementation of a parametric residual iteration for linear interval systems by advanced communication between the system Mathematica and the library C-XSC supporting rigorous complex interval arithmetic. An example of AC electrical circuit illustrates the use of the presented software.* This work was partly supported by the DFG grant GZ:...
A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation
We present an iterative method based on an infinite dimensional adaptation of the successive overrelaxation (SOR) algorithm for solving the 2-D neutron transport equation. In a wide range of application, the neutron transport operator admits a Self-Adjoint and m-Accretive Splitting (SAS). This splitting leads to an ADI-like iterative method which converges unconditionally and is equivalent to a fixed point problem where the operator is a 2 by 2 matrix...
A spatially sixth-order hybrid -CCD method for solving time fractional Schrödinger equations
We consider highly accurate schemes for nonlinear time fractional Schrödinger equations (NTFSEs). While an strategy is employed for approximating the Caputo fractional derivative in the temporal direction, compact CCD finite difference approaches are incorporated in the space. A highly effective hybrid -CCD method is implemented successfully. The accuracy of this linearized scheme is order six in space, and order in time, where is the order of the Caputo fractional derivative involved. It...
A special finite element method based on component mode synthesis
The goal of our paper is to introduce basis functions for the finite element discretization of a second order linear elliptic operator with rough or highly oscillating coefficients. The proposed basis functions are inspired by the classic idea of component mode synthesis and exploit an orthogonal decomposition of the trial subspace to minimize the energy. Numerical experiments illustrate the effectiveness of the proposed basis functions.
A special Gaussian rule for trigonometric polynomials.
A spectral characterization of the behavior of discrete time AR–representations over a finite time interval
In this paper we investigate the behavior of the discrete time AR (Auto Regressive) representations over a finite time interval, in terms of the finite and infinite spectral structure of the polynomial matrix involved in the AR-equation. A boundary mapping equation and a closed formula for the determination of the solution, in terms of the boundary conditions, are also gived.
A spectral Galerkin approximation of the Orr-Sommerfeld eigenvalue problem in a semi-finite domain.
A spectral method for the eigenvalue problem for elliptic equations.
A spectral regularization method for a Cauchy problem of the modified Helmholtz equation.
A spectral-Tau approximation for the Stokes and Navier-Stokes equations
A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations
In this paper we solve the time-dependent incompressible Navier-Stokes equations by splitting the non-linearity and incompressibility, and using discontinuous or continuous finite element methods in space. We prove optimal error estimates for the velocity and suboptimal estimates for the pressure. We present some numerical experiments.
A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations
In this paper we solve the time-dependent incompressible Navier-Stokes equations by splitting the non-linearity and incompressibility, and using discontinuous or continuous finite element methods in space. We prove optimal error estimates for the velocity and suboptimal estimates for the pressure. We present some numerical experiments.
A spring-dashpot system for modelling lung tumour motion in radiotherapy.
A stability analysis for finite volume schemes applied to the Maxwell system
We present in this paper a stability study concerning finite volume schemes applied to the two-dimensional Maxwell system, using rectangular or triangular meshes. A stability condition is proved for the first-order upwind scheme on a rectangular mesh. Stability comparisons between the Yee scheme and the finite volume formulation are proposed. We also compare the stability domains obtained when considering the Maxwell system and the convection equation.
A Stability Analysis for the Extended Kantorovich Method Applied to the Torsion Problem.
-stability and numerical solution of abstract differential equations
A stability test for real polynomials.
A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes
It is well known that the classical local projection method as well as residual-based stabilization techniques, as for instance streamline upwind Petrov-Galerkin (SUPG), are optimal on isotropic meshes. Here we extend the local projection stabilization for the Navier-Stokes system to anisotropic quadrilateral meshes in two spatial dimensions. We describe the new method and prove an a priori error estimate. This method leads on anisotropic meshes to qualitatively better convergence behavior...