An overview of numerically reliable algorithms for model reduction is presented. The covered topics are the reduction of stable and unstable linear systems as well as the computational aspects of frequency weighted model reduction. The presentation of available software tools focuses on a recently developed Fortran library RASP-MODRED implementing a new generation of numerically reliable algori...

A propagating interface can develop corners and discontinuities as it advances. The level set algorithm such as the fast marching method (FMM) has been extensively applied in simulating advancing fronts. However, it is a rstorder scheme and hard to incorporate higher-order schemes in realistic media; it costs O(N log2N), where N is the number of grid points. The article is concerned with the de...

(1)  ut −∆u = f in Ω× (0, T ), u = 0 on ∂Ω× (0, T ), u(·, 0) = u0 in Ω. Here u = u(x, t) is a function of spatial variable x ∈ Ω and time variable t ∈ (0, T ). The Laplace differential operator ∆ is taking with respect to the spatial variable. For the simplicity of exposition, we consider only homogenous Dirichlet boundary condition and comment on the adaptation to Neumann and other type of b...

New Runge–Kutta–Nyström methods especially designed for the numerical integration of perturbed oscillators are presented in this paper. They are capable of exactly integrating the harmonic or unperturbed oscillator. We construct an embedded 4(3) RKN pair that is based on the FSAL property. The new method is much more efficient than previously derived RKN methods for some subclasses of problems....

Article history: Received 15 April 2011 Received in revised form 16 February 2012 Accepted 13 March 2012 Available online 3 April 2012

The lattice Boltzmann equations for the linear diffusion modeling in cases of D2Q5, D2Q7 and D2Q9 lattices are considered. Families of the numerical schemes with the dependence on scalar parameter are introduced. The stability analysis of schemes is performed in parameter space. The stability is studied numerically by von Neumann method. Optimal parameter values for the presented families are d...

A high order version of a diffuse approximate meshless method has been implemented and tested on two problems, namely diffusion and transport diffusion two-dimensional equations. It is shown that the fourth-order approximation greatly improves the numerical solution. 2006 Elsevier Inc. All rights reserved.