In [13], we had performed numerical comparisons for different time stepping schemes for the incompressible Navier-Stokes equations. In this paper, we present the numerical analysis in the context of the Navier-Stokes equations for a new time-stepping θ-scheme which has been recently proposed by Glowinski [5]. Like the well-known classical FractionalStep-θ-scheme which had been introduced by Glo...

This paper presents a complete finite volume method for the Cahn–Hilliard and Kuramoto– Sivashinsky type of equations. The spatial discretization is high-order accurate and suitable for general unstructured grids. The time integration is addressed by means of implicit an implicit–explicit fourth order Runge–Kutta schemes, with error control and adaptive time-stepping. The outcome is a practical...

We present a class of numerical methods for the reaction-diffusion-chemotaxis system which is significant for biological and chemistry pattern formation problems. To solve reactiondiffusion-chemotaxis systems, efficient and reliable numerical algorithms are essential for pattern generations. Along with the implementation of the method of lines, implicit or semi-implicit schemes are typical time...

<p style='text-indent:20px;'>Efficient simulation of SDEs is essential in many applications, particularly for ergodic systems that demand efficient both short-time dynamics and large-time statistics. However, locally Lipschitz often require special treatments such as implicit schemes with small time-steps to accurately simulate the measures. We introduce a framework construct inference-ba...

In this work we present and analyse a time discretisation strategy for linear wave equations t hat aims at using locally in space the most adapted among family of implicit or explicit centered second order schemes. The proposed schemes is to domain decomposition methods such as mortar element method. They correspond that case local stepping. We show that, if some regularity properties solution ...

In this paper, we propose and analyze a first-order second-order time-stepping schemes for the anisotropic phase-field dendritic crystal growth model. The proposed are based on an auxiliary variable approach Allen-Cahn equation delicate treatment of terms coupling temperature equation. idea former is to introduce suitable variables facilitate construction high order stable large class gradient ...