This paper presents an overview of high-order implicit time integration methods and their associated properties with a specific focus on their application to computational fluid dynamics. A framework is constructed for the development and optimization of general implicit time integration methods, specifically including linear multistep, Runge-Kutta, and multistep Runge-Kutta methods. The analys...

Explicit stabilized methods for stiff ordinary differential equations have a long history. Proposed in the early 1960s and developed during 40 years for the integration of stiff ordinary differential equations, these methods have recently been extended to implicit-explicit or partitioned type methods for advection-diffusion-reaction problems, and to efficient explicit solvers for stiff mean-squ...

Modeling methods for Cyber-Physical Systems (CPS) originate in various engineering fields, and are difficult to use together due to their heterogeneity. Inconsistencies between mutually oblivious models and analyses often lead to implicit design errors, which may cause catastrophic failures of critical CPS. Such consistency issues are not fully solved by the state-of-the-art integration methods...

Computing semantic relatedness of natural language texts is a key component of tasks such as information retrieval and summarization, and often depends on knowledge from a broad range of real-world concepts and relationships. We address this knowledge integration issue with a method of computing semantic relatedness using personalized PageRank (random walks) on a graph derived from Wikipedia. T...

The efficiency and accuracy are usually regarded as two general indices to check capability of a numerical method with respect to the time integration. The traditional numerical manifold method (NMM) employs implicit scheme to obtain high computational accuracy, but the efficiency is relatively low, especially when the iterations of contacts are involved. In this paper, the temporal coupled exp...

The purpose of this work was to investigate the utility of implicit integration methods for molecular dynamics (MD) simulation. Implicit methods were investigated in an attempt to address the bottleneck associated with short, stability-limited step size lengths available to the explicit methods currently in widespread use. Two implicit methods were compared to the current standard for time inte...

In this paper new implicit higher order accuracy (N-IHOA) time integration based on assumption of constant time step is presented for dynamic analysis. This method belongs to the category of the multi time step integrations. Here, current displacement and velocity are assumed to be functions of the velocities and accelerations of several previous time steps, respectively. This definition causes...

In this paper, we introduce the concept of constant time updateability for the functional operations that can be used for constructing functions. We believe that constant time updateability will be important in the future for guaranteeing interactive modeling of implicit surfaces that are defined by functional construction of functions. We have developed several tests to determine if a function...

This study investigates the effect of four types of oral corrective feedback, namely, explicit elicitation, implicit elicitation, explicit recast and implicit recast on the most commonly mispronounced phonological features among Iranian EFL learners through immediate uptake and retention. Five classes were randomly categorized into four experimental groups and one control group, each with 18 in...

The stationary Navier-Stokes equations are solved in 2D with semi-implicit Runge-Kutta schemes, where explicit time-integration in the streamwise direction is combined with implicit integration in the body-normal direction. For model problems stability restrictions and convergence properties are studied. Numerical experiments for the ow over a at plate show that the number of iterations for the...