New Computational Algorithms for Analyzing the Stability of the Differential Equations System

In this paper we show how to improve the approximate solution of the large Lyapunov equation obtained by an arbitrary method. Moreover, we propose a new method based on refinement process and Weighted Arnoldi algorithm for solving large Lyapunov matrix equation. Finally, some numerical results will be reported to illustrate the efficiency of the proposed method

Stability Analysis of Distributed Order Fractional Differential Equations

We analyze the stability of three classes of distributed order fractional differential equations (DOFDEs) with respect to the nonnegative density function. In this sense, we discover a robust stability condition for these systems based on characteristic function and new inertia concept of a matrix with respect to the density function. Moreover, we check the stability of a distributed order fractional WINDMI system to illustrate the validity of proposed procedure

A stable pattern of EEG spectral coherence distinguishes children with autism from neuro-typical controls - a large case control study

<p>Abstract</p> <p>Background</p> <p>The autism rate has recently increased to 1 in 100 children. Genetic studies demonstrate poorly understood complexity. Environmental factors apparently also play a role. Magnetic resonance imaging (MRI) studies demonstrate increased brain sizes and altered connectivity. Electroencephalogram (EEG) coherence studies confirm connectivity changes. However, genetic-, MRI- and/or EEG-based diagnostic tests are not yet available. The varied study results likely reflect methodological and population differences, small samples and, for EEG, lack of attention to group-specific artifact.</p> <p>Methods</p> <p>Of the 1,304 subjects who participated in this study, with ages ranging from 1 to 18 years old and assessed with comparable EEG studies, 463 children were diagnosed with autism spectrum disorder (ASD); 571 children were neuro-typical controls (C). After artifact management, principal components analysis (PCA) identified EEG spectral coherence factors with corresponding loading patterns. The 2- to 12-year-old subsample consisted of 430 ASD- and 554 C-group subjects (n = 984). Discriminant function analysis (DFA) determined the spectral coherence factors' discrimination success for the two groups. Loading patterns on the DFA-selected coherence factors described ASD-specific coherence differences when compared to controls.</p> <p>Results</p> <p>Total sample PCA of coherence data identified 40 factors which explained 50.8% of the total population variance. For the 2- to 12-year-olds, the 40 factors showed highly significant group differences (<it>P </it>< 0.0001). Ten randomly generated split half replications demonstrated high-average classification success (C, 88.5%; ASD, 86.0%). Still higher success was obtained in the more restricted age sub-samples using the jackknifing technique: 2- to 4-year-olds (C, 90.6%; ASD, 98.1%); 4- to 6-year-olds (C, 90.9%; ASD 99.1%); and 6- to 12-year-olds (C, 98.7%; ASD, 93.9%). Coherence loadings demonstrated reduced short-distance and reduced, as well as increased, long-distance coherences for the ASD-groups, when compared to the controls. Average spectral loading per factor was wide (10.1 Hz).</p> <p>Conclusions</p> <p>Classification success suggests a stable coherence loading pattern that differentiates ASD- from C-group subjects. This might constitute an EEG coherence-based phenotype of childhood autism. The predominantly reduced short-distance coherences may indicate poor local network function. The increased long-distance coherences may represent compensatory processes or reduced neural pruning. The wide average spectral range of factor loadings may suggest over-damped neural networks.</p

Application of Homotopy Perturbation Method for Fuzzy Linear Systems and Comparison with Adomian’s Decomposition Method

We present an efficient numerical algorithm for solution of the fuzzy linear systems (FLS) based on He’s homotopy perturbation method (HPM). Moreover, the convergence properties of the proposed method have been analyzed and also comparisons are made between Adomian’s decomposition method (ADM) and the proposed method. The results reveal that our method is effective and simple

A New Algorithm for Solving Large-Scale Generalized Eigenvalue Problem Based on Projection Methods

In this paper, we consider four methods for determining certain eigenvalues and corresponding eigenvectors of large-scale generalized eigenvalue problems which are located in a certain region. In these methods, a small pencil that contains only the desired eigenvalue is derived using moments that have obtained via numerical integration. Our purpose is to improve the numerical stability of the moment-based method and compare its stability with three other methods. Numerical examples show that the block version of the moment-based (SS) method with the Rayleigh–Ritz procedure has higher numerical stability than respect to other methods

An Efficient Explicit Decoupled Group Method for Solving Two–Dimensional Fractional Burgers’ Equation and Its Convergence Analysis

In this paper, the Crank–Nicolson (CN) and rotated four-point fractional explicit decoupled group (EDG) methods are introduced to solve the two-dimensional time–fractional Burgers’ equation. The EDG method is derived by the Taylor expansion and 45° rotation of the Crank–Nicolson method around the x and y axes. The local truncation error of CN and EDG is presented. Also, the stability and convergence of the proposed methods are proved. Some numerical experiments are performed to show the efficiency of the presented methods in terms of accuracy and CPU time

Thermodynamic analysis of medium pressure reciprocating natural gas expansion engines

Natural gas pressure has to be reduced from medium pressure of 1.724 MPa (250 psia) to lower pressure of 0.414 MPa (60 psia) at Town Border pressure reduction Station (TBS). Currently, the pressure reduction is carried out by throttling valves while considerable amount of pressure energy is wasted. One of the equipment which could be used to recover this waste energy is the reciprocating expansion engine. The purpose of this research is to simulate one-sided reciprocating expansion engine thermodynamically for TBS pressure range. The simulation is based on first law of thermodynamics, conversation of mass and ideal gas assumptions. The model could predict in-cylinder pressure and in-cylinder temperature at various crank angles. In addition, the effects of the engine geometrical characteristics, such as intake and exhaust port area and ports timing on the Indicated work per cycle output are investigated