STUDYING THE STABILITY BY USING LOCAL LINEARIZATION METHOD

In this paper we study the stability of one of a non linear autoregressive model with trigonometric term by using local linearization method proposed by Tuhro Ozaki .We find the singular point ,the stability of the singular point and the limit cycle. We conclude that the proposed model under certain conditions have a non-zero singular point which is a asymptotically salable ( when 0 ) and have an orbitaly stable limit cycle . Also we give some examples in order to explain the method. Key Words : Non-linear Autoregressive model; Limit cycle; singular point; Stability.

Study of Activation Energy on the Movement of Gyrotactic Microorganism in a Magnetized Nanofluids Past a Porous Plate

The present study deals with the swimming of gyrotactic microorganisms in a nanofluid past a stretched surface. The combined effects of magnetohydrodynamics and porosity are taken into account. The mathematical modeling is based on momentum, energy, nanoparticle concentration, and microorganisms’ equation. A new computational technique, namely successive local linearization method (SLLM), is used to solve nonlinear coupled differential equations. The SLLM algorithm is smooth to establish and employ because this method is based on a simple univariate linearization of nonlinear functions. The numerical efficiency of SLLM is much powerful as it develops a series of equations which can be subsequently solved by reutilizing the data from the solution of one equation in the next one. The convergence was improved through relaxation parameters in the study. The accuracy of SLLM was assured through known methods and convergence analysis. A comparison of the proposed method with the existing literature has also been made and found an excellent agreement. It is worth mentioning that the successive local linearization method was found to be very stable and flexible for resolving the issues of nonlinear magnetic materials processing transport phenomena.

Numerical Investigation on the Swimming of Gyrotactic Microorganisms in Nanofluids through Porous Medium over a Stretched Surface

In this article, the effects of swimming gyrotactic microorganisms for magnetohydrodynamics nanofluid using Darcy law are investigated. The numerical results of nonlinear coupled mathematical model are obtained by means of Successive Local Linearization Method. This technique is based on a simple notion of the decoupling systems of equations utilizing the linearization of the unknown functions sequentially according to the order of classifying the system of governing equations. The linearized equations, that developed a sequence of linear differential equations along with variable coefficients, were solved by employing the Chebyshev spectral collocation method. The convergence speed of the SLLM technique can be willingly upgraded by successive applying over relaxation method. The comparison of current study with available published literature has been made for the validation of obtained results. It is found that the reported numerical method is in perfect accord with the said similar methods. The results are displayed through tables and graphs.

Double-Diffusive Natural Convective Flow of a Nanofluid past an Inclined Wavy Plate in a Non-Darcy Porous Medium

In this paper, the double-diffusive convective flow along an inclined semi-infinite wavy plate in a nanofluid saturated non-Darcy porous medium is investigated numerically. Following Prandtl’s transposition theorem, a coordinate transformation is used to transform the irregular wavy surface into a smooth surface. The convective type thermal boundary condition is taken into account and also the Brownian motion and thermophoresis effects are considered into the present nanofluid model. The governing transport equations are initially reshaped into a system of coupled ordinary differential equations by choosing suitable similarity transformations and then solved numerically by using the Spectral Local Linearization Method (SLLM). The effects of various flow influenced parameters on the fluid flow, heat and mass transfer characteristics are explored and exhibited graphically.

On stability Conditions of Burr X Autoregressive model

This article deals with proposed nonlinear autoregressive model based on Burr X cumulative distribution function known as Burr X AR (p), we demonstrate stability conditions of the proposed model in terms of its parameters by using dynamical approach known as local linearization method to find stability conditions of a nonzero fixed point of the proposed model, in addition the study demonstrate stability condition of a limit cycle if Burr X AR (1) model have a limit cycle of period greater than one. http://dx.doi.org/10.25130/tjps.24.2019.096

Increase of Critical Mach Number by Local Linearization Method and Airfoil Construction at Subsonic and Transonic Regimes

A symmetrical airfoil has been constructed by local linearization method. A single-point objective function is defined to check the convergence of the method. As an example, the nose and tail zone of supercritical airfoil is fixed and a flat line is placed between them. The optimizable element of the airfoil contour was conjoined with the nose and tail elements of fixed shape at the sections with coordinates xs1= 0.11 and xs2= 0.66, respectively. The optimizable part of airfoil (the fixed chord line) is divided into N=55 segments. The convergence of this method has been shown with the airfoil constructed with higher critical Mach number rather than the initial airfoil. Finally, this airfoil has been compared with the supercritical airfoil NASA SC (2)-0012 at M∞=0.76. At the second part, several airfoils have been constructed and simulated over different Subsonic and Transonic Mach numbers. Finally, the drag coefficient on constructed airfoils have been compared with supercritical airfoil.

An unsteady MHD Maxwell nanofluid flow with convective boundary conditions using spectral local linearization method

The main focus of this study is on unsteady Maxwell nanofluid flow over a shrinking surface with convective and slip boundary conditions. The objective is to give an evaluation of the impact and significance of Brownian motion and thermophoresis when the nanofluid particle volume fraction flux at the boundary is zero. The transformed equations are solved numerically using the spectral local linearization method. We present an analysis of the residual errors to show the accuracy and convergence of the spectral local linearization method. We explore the effect of magnetic field and thermophoresis parameters on the heat transfer rate. We show, among other results, that an increase in particle Brownian motion leads to a decrease in the concentration profiles but concentration profiles increase with the increasing value of thermophoresis parameter

Estimation and Analysis of Vehicle Lateral Stability Region With Both Front and Rear Wheel Steering

In this paper, a novel vehicle lateral stability region estimation method considering both front and rear wheel steering is introduced. Vehicle lateral stability regions are estimated by a local linearization method, which guarantees both vehicle local stability and handling stability. The impacts of front and rear wheel steering angles on stability region estimations are formulated and discussed. To quantitatively explain the shifting feature of stability regions under different front/rear steering angles, an explicit analysis about how the equilibrium points and the geometric centers of stability regions change with respect to different steering angles is formulated. The obtained relationship enables the estimation of stability regions in real time for varying front/rear steering angles. The additional rear wheel steering helps to maintain vehicle states stay within estimated stability regions. To show the effectiveness of the proposed real-time stability region estimation method and stability analysis, a Simulink and CarSim® co-simulation is applied to verify that vehicle states are covered within varying stability regions for a single lane change maneuver.