This paper investigates the implementation of Variational Iteration Method (VIM) to practical and higher order nonlinear equations in kind of Korteweg-de-Vries (KdV) equation. The obtained solutions from thirdand fourth-order modified KdV are compared with the exact and Homotopy Perturbation Method (HPM) solutions. Results illustrate the efficiency and capability of VIM to solve high order nonl...

We consider well-known decomposition techniques for multistage stochastic programming and a new scheme based on normal solutions for stabilizing calculations as the iteration process progresses. The given algorithms combine ideas from finite perturbation of convex programs and level bundle methods to regularize the so-called forward step of these decomposition methods. In contrast to other regu...

Water pollution is a major global problem that requires ongoing evaluation and revision of water resource policies at all levels, in order to create a healthy living environment. Differential equations are an effective way to analyze such situations. In this paper a system of linear equations with interconnecting pipes is considered for analyzing the pollution of system of lakes through differe...

This paper presents a stochastic iteration algorithm solving the global illumination problem, where the random sampling is governed by classical importance sampling and also by the Metropolis method. Point pairs where radiance transfer takes place are obtained with random ray shooting. Ray shooting can mimic the source radiance and the geometric factor, but not the receiving capability of the t...

In bioinformatics, sequence alignment is one of the most common problems. Multiple sequence alignment is an NP (nondeterministic polynomial time) problem, which requires further study and exploration. The chaos optimization algorithm is a type of chaos theory, and a procedure for combining the genetic algorithm (GA), which uses ergodicity, and inherent randomness of chaotic iteration. It is an ...

The Banach–Picard iteration is widely used to find fixed points of locally contractive (LC) maps. This article extends the distributed settings; specifically, we assume map which point sought be average individual (not necessarily LC) maps held by a set agents linked communication network. An additional difficulty that LC not assumed come from an underlying optimization problem, prevents exploi...

This paper presents a stochastic iteration algorithm solving the global illumination problem, where the random sampling is governed by classical importance sampling and also by the Metropolis method. Point pairs where radiance transfer takes place are obtained with random ray shooting. Ray shooting can mimic the source radiance and the geometric factor, but not the receiving capability of the t...

Many exploration and drilling applications would benefit from a robust method of integrating vertical seismic profile (VSP) and seismic data to estimate interval velocity. In practice, both VSP and seismic data contain random and correlated errors, and integration methods which fail to account for both types of error encounter problems. We present a nonlinear, tomography-like least-squares algo...

The iterative nature of the expectation maximization (EM) algorithm presents a challenge for privacy-preserving estimation, as each iteration increases the amount of noise needed. We propose a practical private EM algorithm that overcomes this challenge using two innovations: (1) a novel moment perturbation formulation for differentially private EM (DP-EM), and (2) the use of two recently devel...

Most of the localization algorithms have performed localization utilizing absolute point-topoint distance estimates. If the sensor network is not cooperative, there’s no information about the strength of the original signal so that the location of a target node is hard to be found. It allows ratiometric location algorithm to be proposed. GPS algorithm give accurate location of unknown node, how...