Numerical solution of two delays Volterra Integral Equations is considered and the stability is studied on a nonlinear test equation by carrying out a parallel investigation both on the continuous and the discrete problem.

In the present discussion a no-slip boundary condition for walls with a tangential movement is derived. The resulting closure is local, conserves mass exactly and is second order accurate with respect to the grid spacing. In addition it avoids the numerical instabilities observed for other types...

We observe that in a simple one-dimensional polynomial optimization problem (POP), the ‘optimal’ values of semidefinite programming (SDP) relaxation problems reported by the standard SDP solvers converge to the optimal value of the POP, while the true optimal values of SDP relaxation...

Forced internal waves at the interface of a two-layer incompressible fluid in a two-dimensional domain with rigid horizontal boundaries are studied. The lower boundary is assumed to have a small obstruction. We derive a time-dependent forced modified KdV equation when the KdV theory fails and...

In this paper two stable and explicit numerical methods to integrate the one-dimensional (1D) advection–diffusion equation are presented. These schemes are stable by design and follow the main general concept behind the semi-Lagrangian method by constructing a virtual grid where the explicit...

Artificial dissipation is a well known tool for the improvement of stability of numerical algorithms. However, the use of this technique affects the accuracy of the computation. We analyse various approaches proposed for enhancement of the Lattice Boltzmann Methods’ (LBM) stability. In...

An extended numerical scheme for the simulation of fluid flows by means of a lattice Boltzmann (LB) method is introduced. It is conceptually related to the lattice BGK scheme, which it enhances by a regularization step. The result is a numerical scheme that is both more accurate and more stable...

An electrical power system usually includes machines with their regulators and controls linked through power lines, transformers, capacitor banks, reactors, and loads. In stability analysis, two distinct strategies are possible for solving the differential equations and network equations...

A finite difference approximation method for the numerical study of the evolution equations for magnetoelastic materials is proposed and results concerning the numerical stability are established. Experiments on a specific test problem are carried out mainly to investigate on some evolutive...

Reaction–diffusion equations are fundamental in modelling several natural phenomena. The numerical schemes used to solve these equations often suffer from numerical stability problems. In this paper, a new type of algorithm to solve the diffusion equation in a stable and explicit manner is...