Search results for: Taylor’s series of fractional order
5993 Derivation of Fractional Black-Scholes Equations Driven by Fractional G-Brownian Motion and Their Application in European Option Pricing
Authors: Changhong Guo, Shaomei Fang, Yong He
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In this paper, fractional Black-Scholes models for the European option pricing were established based on the fractional G-Brownian motion (fGBm), which generalizes the concepts of the classical Brownian motion, fractional Brownian motion and the G-Brownian motion, and that can be used to be a tool for considering the long range dependence and uncertain volatility for the financial markets simultaneously. A generalized fractional Black-Scholes equation (FBSE) was derived by using the Taylor’s series of fractional order and the theory of absence of arbitrage. Finally, some explicit option pricing formulas for the European call option and put option under the FBSE were also solved, which extended the classical option pricing formulas given by F. Black and M. Scholes.Keywords: European option pricing, fractional Black-Scholes equations, fractional G-Brownian motion, Taylor’s series of fractional order, uncertain volatility.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8365992 Stability of Interval Fractional-order Systems with Order 0 < α < 1
Authors: Hong Li, Shou-ming Zhong, Hou-biao Li
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In this paper, some brief sufficient conditions for the stability of FO-LTI systems dαx(t) dtα = Ax(t) with the fractional order are investigated when the matrix A and the fractional order α are uncertain or both α and A are uncertain, respectively. In addition, we also relate the stability of a fractional-order system with order 0 < α ≤ 1 to the stability of its equivalent fractional-order system with order 1 ≤ β < 2, the relationship between α and β is presented. Finally, a numeric experiment is given to demonstrate the effectiveness of our results.
Keywords: Interval fractional-order systems, linear matrix inequality (LMI), asymptotical stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 36005991 Fractional Order Feedback Control of a Ball and Beam System
Authors: Santosh Kr. Choudhary
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In this paper, fractional order feedback control of a ball beam model is investigated. The ball beam model is a particular example of the double Integrator system having strongly nonlinear characteristics and unstable dynamics which make the control of such system a challenging task. Most of the work in fractional order control systems are in theoretical nature and controller design and its implementation in practice is very small. In this work, a successful attempt has been made to design a fractional order PIλDμcontroller for a benchmark laboratory ball and beam model. Better performance can be achieved using a fractional order PID controller and it is demonstrated through simulations results with a comparison to the classic PID controller.
Keywords: Fractional order calculus, fractional order controller, fractional order system, ball and beam system, PIλDμ controller, modelling, simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 35425990 Solution of Two-Point Nonlinear Boundary Problems Using Taylor Series Approximation and the Ying Buzu Shu Algorithm
Authors: U. C. Amadi, N. A. Udoh
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One of the major challenges faced in solving initial and boundary problems is how to find approximate solutions with minimal deviation from the exact solution without so much rigor and complications. The Taylor series method provides a simple way of obtaining an infinite series which converges to the exact solution for initial value problems and this method of solution is somewhat limited for a two point boundary problem since the infinite series has to be truncated to include the boundary conditions. In this paper, the Ying Buzu Shu algorithm is used to solve a two point boundary nonlinear diffusion problem for the fourth and sixth order solution and compare their relative error and rate of convergence to the exact solution.
Keywords: Ying Buzu Shu, nonlinear boundary problem, Taylor series algorithm, infinite series.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4385989 A Design of Fractional-Order PI Controller with Error Compensation
Authors: Mazidah Tajjudin, Norhashim Mohd Arshad, Ramli Adnan
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Fractional-order controller was proven to perform better than the integer-order controller. However, the absence of a pole at origin produced marginal error in fractional-order control system. This study demonstrated the enhancement of the fractionalorder PI over the integer-order PI in a steam temperature control. The fractional-order controller was cascaded with an error compensator comprised of a very small zero and a pole at origin to produce a zero steady-state error for the closed-loop system. Some modification on the error compensator was suggested for different order fractional integrator that can improve the overall phase margin.
Keywords: Fractional-order PI, Ziegler-Nichols tuning, Oustaloup's Recursive Approximation, steam temperature control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22855988 Realization of Fractional-Order Capacitors with Field-Effect Transistors
Authors: Steve Hung-Lung Tu, Yu-Hsuan Cheng
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A novel and efficient approach to realize fractional-order capacitors is investigated in this paper. Meanwhile, a new approach which is more efficient for semiconductor implementation of fractional-order capacitors is proposed. The feasibility of the approach has been verified with the preliminary measured results.Keywords: Fractional-order, field-effect transistors, RC transmission lines.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 31455987 Observer Based Control of a Class of Nonlinear Fractional Order Systems using LMI
Authors: Elham Amini Boroujeni, Hamid Reza Momeni
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Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach. Finally, the simulation results demonstrate validity and effectiveness of the proposed observer based controller.Keywords: Fractional order calculus, Fractional order observer, Linear matrix inequality, Nonlinear Systems, Observer based Controller.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 28675986 Approximated Solutions of Two-Point Nonlinear Boundary Problem by a Combination of Taylor Series Expansion and Newton Raphson Method
Authors: Chinwendu. B. Eleje, Udechukwu P. Egbuhuzor
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One of the difficulties encountered in solving nonlinear Boundary Value Problems (BVP) by many researchers is finding approximated solutions with minimum deviations from the exact solutions without so much rigor and complications. In this paper, we propose an approach to solve a two point BVP which involves a combination of Taylor series expansion method and Newton Raphson method. Furthermore, the fourth and sixth order approximated solutions are obtained and we compare their relative error and rate of convergence to the exact solution. Finally, some numerical simulations are presented to show the behavior of the solution and its derivatives.
Keywords: Newton Raphson method, non-linear boundary value problem, Taylor series approximation, Michaelis-Menten equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2985985 Stability Analysis of Fractional Order Systems with Time Delay
Authors: Hong Li, Shou-Ming Zhong, Hou-Biao Li
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In this paper, we mainly study the stability of linear and interval linear fractional systems with time delay. By applying the characteristic equations, a necessary and sufficient stability condition is obtained firstly, and then some sufficient conditions are deserved. In addition, according to the equivalent relationship of fractional order systems with order 0 < α ≤ 1 and with order 1 ≤ β < 2, one may get more relevant theorems. Finally, two examples are provided to demonstrate the effectiveness of our results.
Keywords: Fractional order systems, Time delay, Characteristic equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 36475984 On Fractional (k,m)-Deleted Graphs with Constrains Conditions
Authors: Sizhong Zhou, Hongxia Liu
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Let G be a graph of order n, and let k 2 and m 0 be two integers. Let h : E(G) [0, 1] be a function. If e∋x h(e) = k holds for each x V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G) k + m + m k+1 , n 4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)} n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.
Keywords: Graph, degree condition, fractional k-factor, fractional (k, m)-deleted graph.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11915983 A Neighborhood Condition for Fractional k-deleted Graphs
Authors: Sizhong Zhou, Hongxia Liu
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Abstract–Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k +3- 42(k - 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if there exists a fractional k-factor after deleting any edge of G. In this paper, it is proved that G is a fractional k-deleted graph if G satisfies δ(G) ≥ k + 1 and |NG(x) ∪ NG(y)| ≥ 1 2 (n + k - 2) for each pair of nonadjacent vertices x, y of G.
Keywords: Graph, minimum degree, neighborhood union, fractional k-factor, fractional k-deleted graph.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10535982 Perturbation in the Fractional Fourier Span due to Erroneous Transform Order and Window Function
Authors: Sukrit Shankar, Chetana Shanta Patsa, Jaydev Sharma
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Fractional Fourier Transform is a generalization of the classical Fourier Transform. The Fractional Fourier span in general depends on the amplitude and phase functions of the signal and varies with the transform order. However, with the development of the Fractional Fourier filter banks, it is advantageous in some cases to have different transform orders for different filter banks to achieve better decorrelation of the windowed and overlapped time signal. We present an expression that is useful for finding the perturbation in the Fractional Fourier span due to the erroneous transform order and the possible variation in the window shape and length. The expression is based on the dependency of the time-Fractional Fourier span Uncertainty on the amplitude and phase function of the signal. We also show with the help of the developed expression that the perturbation of span has a varying degree of sensitivity for varying degree of transform order and the window coefficients.Keywords: Fractional Fourier Transform, Perturbation, Fractional Fourier span, amplitude, phase, transform order, filterbanks.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14595981 Projective Synchronization of a Class of Fractional-Order Chaotic Systems
Authors: Zahra Yaghoubi, Nooshin Bigdeli, Karim Afshar
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This paper at first presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. After that a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization" for a class of fractional-order chaotic systems via a scalar transmitted signal. Genesio_Tesi and Duffing systems are used to illustrate the effectiveness of the proposed synchronization method. Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18015980 Application of Fractional Model Predictive Control to Thermal System
Authors: Aymen Rhouma, Khaled Hcheichi, Sami Hafsi
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The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller.
Keywords: Fractional model predictive control, fractional order systems, thermal system.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12085979 Lyapunov Type Inequalities for Fractional Impulsive Hamiltonian Systems
Authors: Kazem Ghanbari, Yousef Gholami
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This paper deals with study about fractional order impulsive Hamiltonian systems and fractional impulsive Sturm-Liouville type problems derived from these systems. The main purpose of this paper devotes to obtain so called Lyapunov type inequalities for mentioned problems. Also, in view point on applicability of obtained inequalities, some qualitative properties such as stability, disconjugacy, nonexistence and oscillatory behaviour of fractional Hamiltonian systems and fractional Sturm-Liouville type problems under impulsive conditions will be derived. At the end, we want to point out that for studying fractional order Hamiltonian systems, we will apply recently introduced fractional Conformable operators.Keywords: Fractional derivatives and integrals, Hamiltonian system, Lyapunov type inequalities, stability, disconjugacy.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15185978 Finite-time Stability Analysis of Fractional-order with Multi-state Time Delay
Authors: Liqiong Liu, Shouming Zhong
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In this paper, the finite-time stabilization of a class of multi-state time delay of fractional-order system is proposed. First, we define finite-time stability with the fractional-order system. Second, by using Generalized Gronwall's approach and the methods of the inequality, we get some conditions of finite-time stability for the fractional system with multi-state delay. Finally, a numerical example is given to illustrate the result.
Keywords: Finite-time stabilization, fractional-order system, Gronwall inequality.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18935977 Measurement Fractional Order Sallen-Key Filters
Authors: Ahmed Soltan, Ahmed G. Radwan, Ahmed M. Soliman
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This work aims to generalize the integer order Sallen-Key filters into the fractional-order domain. The analysis in the case of two different fractional-order elements introduced where the general transfer function becomes four terms which is unusual in the conventional case. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced and closed forms for the filter critical frequencies are driven. Finally, different examples for the fractional order Sallen-Key filter design are presented with circuit simulations using ADS where a great matching between the numerical and simulation results is obtained.
Keywords: Analog Filter, Low-Pass Filter, Fractance, Sallen-Key, Stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 31305976 Notes on Fractional k-Covered Graphs
Authors: Sizhong Zhou, Yang Xu
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A graph G is fractional k-covered if for each edge e of G, there exists a fractional k-factor h, such that h(e) = 1. If k = 2, then a fractional k-covered graph is called a fractional 2-covered graph. The binding number bind(G) is defined as follows, bind(G) = min{|NG(X)| |X| : ├ÿ = X Ôèå V (G),NG(X) = V (G)}. In this paper, it is proved that G is fractional 2-covered if δ(G) ≥ 4 and bind(G) > 5 3 .Keywords: graph, binding number, fractional k-factor, fractional k-covered graph.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11675975 Synthesis of Digital Circuits with Genetic Algorithms: A Fractional-Order Approach
Authors: Cecília Reis, J. A. Tenreiro Machado, J. Boaventura Cunha
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This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution.
Keywords: Circuit design, fractional-order systems, genetic algorithms, logic circuits.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14155974 Quality Factor Variation with Transform Order in Fractional Fourier Domain
Authors: Sukrit Shankar, Chetana Shanta Patsa, K. Pardha Saradhi, Jaydev Sharma
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Fractional Fourier Transform is a powerful tool, which is a generalization of the classical Fourier Transform. This paper provides a mathematical relation relating the span in Fractional Fourier domain with the amplitude and phase functions of the signal, which is further used to study the variation of quality factor with different values of the transform order. It is seen that with the increase in the number of transients in the signal, the deviation of average Fractional Fourier span from the frequency bandwidth increases. Also, with the increase in the transient nature of the signal, the optimum value of transform order can be estimated based on the quality factor variation, and this value is found to be very close to that for which one can obtain the most compact representation. With the entire mathematical analysis and experimentation, we consolidate the fact that Fractional Fourier Transform gives more optimal representations for a number of transform orders than Fourier transform.Keywords: Fractional Fourier Transform, Quality Factor, Fractional Fourier span, transient signals.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12325973 Backstepping Design and Fractional Derivative Equation of Chaotic System
Authors: Ayub Khan, Net Ram Garg, Geeta Jain
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In this paper, Backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems.
Keywords: Backstepping method, Fractional order, Synchronization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21315972 Synthesis of Logic Circuits Using Fractional-Order Dynamic Fitness Functions
Authors: Cecília Reis, J. A. Tenreiro Machado, J. Boaventura Cunha
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This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution.
Keywords: Circuit design, fractional-order systems, genetic algorithms, logic circuits
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17255971 Relation between Roots and Tangent Lines of Function in Fractional Dimensions: A Method for Optimization Problems
Authors: Ali Dorostkar
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In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions.
Keywords: Tangent line, fractional dimension, root, optimization problem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5535970 An Efficient Collocation Method for Solving the Variable-Order Time-Fractional Partial Differential Equations Arising from the Physical Phenomenon
Authors: Haniye Dehestani, Yadollah Ordokhani
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In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.Keywords: Collocation method, fractional partial differential equations, Legendre-Laguerre functions, pseudo-operational matrix of integration.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10105969 A Necessary Condition for the Existence of Chaos in Fractional Order Delay Differential Equations
Authors: Sachin Bhalekar
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In this paper we propose a necessary condition for the existence of chaos in delay differential equations of fractional order. To explain the proposed theory, we discuss fractional order Liu system and financial system involving delay.
Keywords: Caputo derivative, delay, stability, chaos.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26575968 Fractional-Order PI Controller Tuning Rules for Cascade Control System
Authors: Truong Nguyen Luan Vu, Le Hieu Giang, Le Linh
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The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods.
Keywords: Fractional calculus, fractional–order proportional integral controller, cascade control system, internal model control approach.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15445967 Stability Analysis in a Fractional Order Delayed Predator-Prey Model
Authors: Changjin Xu, Peiluan Li
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In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.
Keywords: Fractional predator-prey model, laplace transform, characteristic equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24905966 Anisotropic Total Fractional Order Variation Model in Seismic Data Denoising
Authors: Jianwei Ma, Diriba Gemechu
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In seismic data processing, attenuation of random noise is the basic step to improve quality of data for further application of seismic data in exploration and development in different gas and oil industries. The signal-to-noise ratio of the data also highly determines quality of seismic data. This factor affects the reliability as well as the accuracy of seismic signal during interpretation for different purposes in different companies. To use seismic data for further application and interpretation, we need to improve the signal-to-noise ration while attenuating random noise effectively. To improve the signal-to-noise ration and attenuating seismic random noise by preserving important features and information about seismic signals, we introduce the concept of anisotropic total fractional order denoising algorithm. The anisotropic total fractional order variation model defined in fractional order bounded variation is proposed as a regularization in seismic denoising. The split Bregman algorithm is employed to solve the minimization problem of the anisotropic total fractional order variation model and the corresponding denoising algorithm for the proposed method is derived. We test the effectiveness of theproposed method for synthetic and real seismic data sets and the denoised result is compared with F-X deconvolution and non-local means denoising algorithm.Keywords: Anisotropic total fractional order variation, fractional order bounded variation, seismic random noise attenuation, Split Bregman Algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10015965 Robust Fractional-Order PI Controller with Ziegler-Nichols Rules
Authors: Mazidah Tajjudin, Mohd Hezri Fazalul Rahiman, Norhashim Mohd Arshad, Ramli Adnan
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In process control applications, above 90% of the controllers are of PID type. This paper proposed a robust PI controller with fractional-order integrator. The PI parameters were obtained using classical Ziegler-Nichols rules but enhanced with the application of error filter cascaded to the fractional-order PI. The controller was applied on steam temperature process that was described by FOPDT transfer function. The process can be classified as lag dominating process with very small relative dead-time. The proposed control scheme was compared with other PI controller tuned using Ziegler-Nichols and AMIGO rules. Other PI controller with fractional-order integrator known as F-MIGO was also considered. All the controllers were subjected to set point change and load disturbance tests. The performance was measured using Integral of Squared Error (ISE) and Integral of Control Signal (ICO). The proposed controller produced best performance for all the tests with the least ISE index.
Keywords: PID controller, fractional-order PID controller, PI control tuning, steam temperature control, Ziegler-Nichols tuning.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 34585964 Rear Separation in a Rotating Fluid at Moderate Taylor Numbers
Authors: S. Damodaran, T. V. S.Sekhar
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The motion of a sphere moving along the axis of a rotating viscous fluid is studied at high Reynolds numbers and moderate values of Taylor number. The Higher Order Compact Scheme is used to solve the governing Navier-Stokes equations. The equations are written in the form of Stream function, Vorticity function and angular velocity which are highly non-linear, coupled and elliptic partial differential equations. The flow is governed by two parameters Reynolds number (Re) and Taylor number (T). For very low values of Re and T, the results agree with the available experimental and theoretical results in the literature. The results are obtained at higher values of Re and moderate values of T and compared with the experimental results. The results are fourth order accurate.Keywords: Navier_Stokes equations, Taylor number, Reynolds number, Higher order compact scheme, Rotating Fluid.
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