duo, siwei lakoba, taras i. zhang, yanzhi

We analytically and numerically investigate the stability and dynamics of the plane wave solutions of the fractional nonlinear Schrödinger (NLS) equation, where the long-range dispersion is described by the fractional Laplacian (−Δ)α/2. The linear stability analysis shows that plane wave solutions in the defocusing NLS are always stable if the powe...

Higham, Nicholas Mary, Théo

Block low-rank (BLR) matrices possess a blockwise low-rank property that can be exploited to reduce the complexity of numerical linear algebra algorithms. The impact of these low-rank approximations on the numerical stability of the algorithms in floating-point arithmetic has not previously been analyzed. We present rounding error analysis for the ...

messina, eleonora vecchio, antonia

In this paper, the asymptotic behaviour of the numerical solution to the Volterra integral equations is studied. In particular, a technique based on an appropriate splitting of the kernel is introduced, which allows one to obtain vanishing asymptotic (transient) behaviour in the numerical solution, consistently with the properties of the analytical...

Orlac'h, Jean-Maxime Darabiha, Nasser Giovangigli, Vincent Franzelli, Benedetta

Considerable progress has been made over the past decades in the modeling of gas-phase synthesis of nanoparticles. However, when the nanoparticles mass fraction is large representing up to 50 % of the mixture mass fraction, some issues can be observed in the self-consistent modeling of the production process. In particular, enthalpy exchanges betwe...

gheorghiu, călin-ioan

We are concerned with the study of some classical spectral collocation methods, mainly Chebyshev and sinc as well as with the new software system Chebfun in computing high order eigenpairs of singular and regular Schrö / dinger eigenproblems. We want to highlight both the qualities as well as the shortcomings of these methods and evaluate them ...

Orlac'ch, Jean-Maxime Darabiha, Nasser Giovangigli, Vincent Franzelli, Benedetta

In most simulations of fine particles in reacting flows, including sooting flames, en-thalpy exchanges between gas and particle phases and differential diffusion between the two phases are most often neglected, since the particle mass fraction is generally very small. However, when the nanoparticles mass fraction is very large representing up to 50...

Crouseilles, Nicolas Einkemmer, Lukas Massot, Josselin

The efficient numerical solution of many kinetic models in plasma physics is impeded by the stiffness of these systems. Exponential integrators are attractive in this context as they remove the CFL condition induced by the linear part of the system, which in practice is often the most stringent stability constraint. In the literature, these schemes...

Yukhno, L. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractFor an overdetermined system of linear algebraic equations, the elimination problem is considered, that is, the problem of calculating a given linear form of a solution of the system without calculating the solution itself. Importantly, this system can be inconsistent; thus, the solution obtained by the least square method is used, that is,...

xing, qinyan yang, qinghao wang, weixuan

This paper presents a step-by-step time integration method for transient solutions of nonlinear structural dynamic problems. Taking the second-order nonlinear dynamic equations as the model problem, this self-starting one-step algorithm is constructed using the Galerkin finite element method (FEM) and Newton&ndash / Raphson iteration, in which it i...

gawronska, elzbieta

Progress in computational methods has been stimulated by the widespread availability of cheap computational power leading to the improved precision and efficiency of simulation software. Simulation tools become indispensable tools for engineers who are interested in attacking increasingly larger problems or are interested in searching larger phase ...