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...

Atmospheric flows are characterized by a large range of length scales as well as strong gradients. The accurate simulation of such flows requires numerical algorithms with high spectral resolution, as well as the ability to provide nonoscillatory solutions across regions of high gradients. These flows exhibit a large range of time scales as well—the slowest waves propagate at the flow velocity ...

Introduction: The neural substrates of temporal processing are not still fully known. The majority of interval timing studies have dealt with this subject in the context of “Explicit timing” (computing the time intervals explicitly). The hypothesis “Implicit timing” (implicitly using temporal processing to improve function) has also proposed. This lesion study addressed explicit and implicit ti...

A collection of methods is presented to adapt a pre-existing time-stepping code to perform various bifurcation-theoretic tasks. It is shown that the implicit linear step of a time-stepping code can serve as a highly effective preconditioner for solving linear systems involving the full Jacobian via conjugate gradient iteration. The methods presented for steady-state solving, continuation, direc...

We formulate the relativistic implicit time-dependent Vlasov-Maxwell’s system based on the simplified implicit Maxwell solver. An implicit finite difference algorithm is developed to solve the Maxwell’s equations and equations of motion without coupling to each other, and is implemented to a newly developed 1d3v code. We test the code against the two stream instability, ion acoustic wave dampin...

In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in...

A fully-implicit numerical method based upon adaptively refined meshes for the simulation of pure materials and binary alloy solidification in 2D is presented. In addition we combine a second-order fully-implicit time discretisation scheme with variable steps size control to obtain an adaptive time and space discretisation method. The superiority of this method, compared to widely used fully-ex...

Flood routing has many applications in engineering projects and helps designers in understanding the flood flow characteristics in river flows. Floods are taken unsteady flows that vary by time and location. Equations governing unsteady flows in waterways are continuity and momentum equations which in case of one-dimensional flow the Saint-Venant hypothesis is considered. Dynamic wave model as ...