We consider the following basic question: a source node wishes to stream an ordered sequence of packets to a collection of receivers, which are in K clusters. A node may send a packet to another node in its own cluster in one time step and to a node in a different cluster in Tc time steps (Tc > 1). Each cluster has two special nodes. We assume that the source and the special nodes in each clust...

this paper presents approximate analytical solutions for nonlinear oscillators using the multi-step homotopy analysis method (msham). the proposed scheme is only a simple modification of the homotopy analysis method, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. several illustrat...

in this paper a novel process monitoring scheme for reducing the type і and type іі error rates in the monitoring phase is proposed. first, the proposed approach uses an augmented data matrix to implement the process dynamic. then, we apply independent component analysis (ica) transformation to the augmented data matrix, and eliminate the outliers using the local outlier factor (lof) algorithm....

In this work, we derive a goal-oriented a posteriori error estimator for the error due to time discretization. As time discretization scheme we consider the fractional step theta method, that consists of three subsequent steps of the one-step theta method. In every sub-step, the full incompressible system has to be solved (in contrast to time integrators of operator splitting type). The resulti...

A simple accelerated third-order Runge-Kutta-type, fixed time step, integration scheme that uses just two function evaluations per step is developed. Because of the lower number of function evaluations, the scheme proposed herein has a lower computational cost than the standard third-order Runge-Kutta scheme while maintaining the same order of local accuracy. Numerical examples illustrating the...

We deal with the numerical simulation of a motion of viscous compressible fluids. We discretize the governing Navier–Stokes equations by the backward difference formula – discontinuous Galerkin finite element (BDF-DGFE) method, which exhibits a sufficiently stable, efficient and accurate numerical scheme. The BDF-DGFE method requires a solution of one linear algebra system at each time step. In...

This paper discusses a new volumeand volume concentration–conserving, positive-definite, unconditionally stable iterative numerical scheme for solving temporary cloud/raindrop coalescence followed by breakup and the coupling of the scheme with an existing noniterative, volumeand volume concentration– conserving collision/coalescence (coagulation) scheme. The breakup scheme alone compares nearly...