Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though the Lyapunov methods are applied. There has to find a positive definite Lyapunov function, and its derivative function has to be negative definite. A new approach had been tested in several …
In this paper, several combination algorithms between Partial Update LMS (PU LMS) methods and previously proposed algorithm (New Variable Length LMS (NVLLMS)) have been developed. Then, the new sets of proposed algorithms were applied to an Acoustic Echo Cancellation system (AEC) in order to decrease the filter coefficients, decrease the convergence time, and enhance its performance in terms of Mean Square Error (MSE) and Echo Return Loss Enhancement (ERLE). These proposed algorithms will use the Echo Return Loss Enhancement (ERLE) to control the operation of filter's coefficient length variation. In addition, the time-varying step size is used.The total number of coefficients required was reduced by about 18% , 10% , 6%
... Show MoreThis paper presents a comparative study of two learning algorithms for the nonlinear PID neural trajectory tracking controller for mobile robot in order to follow a pre-defined path. As simple and fast tuning technique, genetic and particle swarm optimization algorithms are used to tune the nonlinear PID neural controller's parameters to find the best velocities control actions of the right wheel and left wheel for the real mobile robot. Polywog wavelet activation function is used in the structure of the nonlinear PID neural controller. Simulation results (Matlab) and experimental work (LabVIEW) show that the proposed nonlinear PID controller with PSO
learning algorithm is more effective and robust than genetic learning algorithm; thi
The present study considers to confirming the applicability of flow with double-sided square lid driven cavity flow by using the lattice Boltzmann equation with moment-based boundary conditions for no slip boundaries. The boundary conditions are applied over the hydrodynamic moments of the lattice Boltzmann equations locally at each node. The investigation is carried out numerically for both single and multiple relaxation time models. To simulate two-sided lid driven-cavity flow, the top and bottom walls are moving with constant velocity while other walls are stationary. Various Reynolds numbers are used in a range of 100 and up to 5000. The present method shows the effect of the moving boundaries on the two symmetrical cavities t
... Show MoreThe aim of this paper is to evaluate the rate of contamination in soils by using accurate numerical method as a suitable tool to evaluate the concentration of heavy metals in soil. In particular, 2D –interpolation methods are applied in the models of the spread the metals in different direction.The paper illustrates the importance of the numerical method in different applications, especially nvironment contamination. Basically, there are many roles for approximating functions. Thus, the approximating of function namely the analytical expression may be expressed; the most common type being is polynomials, which are the easy implemented and simplest methods of approximation. In this paper the divided difference formula is used and extended
... Show MoreJournal of Physics: Conference Series PAPER • THE FOLLOWING ARTICLE ISOPEN ACCESS Estimate the Rate of Contamination in Baghdad Soils By Using Numerical Method Luma Naji Mohammed Tawfiq1, Nadia H Al-Noor2 and Taghreed H Al-Noor1 Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series, Volume 1294, Issue 3 Citation Luma Naji Mohammed Tawfiq et al 2019 J. Phys.: Conf. Ser. 1294 032020 DOI 10.1088/1742-6596/1294/3/032020 DownloadArticle PDF References Download PDF 135 Total downloads 88 total citations on Dimensions. Turn on MathJax Share this article Share this content via email Share on Facebook (opens new window) Share on Twitter (opens new window) Share on Mendeley (opens new window) Hide article and author
... Show MoreVolterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained
... Show MoreBackground: The primary stability of the dental implant is a crucial factor determining the ability to initiate temporary implant-supported prosthesis and for subsequent successful osseointegration, especially in the maxillary non-molar sites. This study assessed the reliability of the insertion torque of dental implants by relating it to the implant stability quotient values measured by the Osstell device. Material and methods: This study included healthy, non-smoker patients with no history of diabetes or other metabolic, or debilitating diseases that may affect bone healing, having non-restorable fractured teeth and retained roots in the maxillary non-molar sites. Primary dental implant stability was evaluated using a torque ratc
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