Search results for: fuzzy differential equations
2532 Numerical Solution of Volterra Integro-differential Equations of Fractional Order by Laplace Decomposition Method
Authors: Changqing Yang, Jianhua Hou
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In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.
Keywords: Integro-differential equations, Laplace transform, fractional derivative, adomian polynomials, pade appoximants.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16482531 On the Efficiency of Five Step Approximation Method for the Solution of General Third Order Ordinary Differential Equations
Authors: N. M. Kamoh, M. C. Soomiyol
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In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.
Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6452530 Exterior Calculus: Economic Growth Dynamics
Authors: Troy L. Story
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Mathematical models of dynamics employing exterior calculus are mathematical representations of the same unifying principle; namely, the description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a characteristic tangent vector (vortex vector) which define transformations of the system. Using this principle, a mathematical model for economic growth is constructed by proposing a characteristic differential one-form for economic growth dynamics (analogous to the action in Hamiltonian dynamics), then generating a pair of characteristic differential equations and solving these equations for the rate of economic growth as a function of labor and capital. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian for economic growth dynamics is obtained.
Keywords: Differential geometry, exterior calculus, Hamiltonian geometry, mathematical economics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14752529 On the Fuzzy Difference Equation xn+1 = A +
Authors: Qianhong Zhang, Lihui Yang, Daixi Liao,
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In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.
Keywords: Fuzzy difference equation, boundedness, persistence, equilibrium point, asymptotic behaviour.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16012528 On a New Inverse Polynomial Numerical Scheme for the Solution of Initial Value Problems in Ordinary Differential Equations
Authors: R. B. Ogunrinde
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This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.Keywords: Differential equations, Numerical, Initial value problem, Polynomials.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17582527 Positive Solutions of Initial Value Problem for the Systems of Second Order Integro-Differential Equations in Banach Space
Authors: Lv Yuhua
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In this paper, by establishing a new comparison result, we investigate the existence of positive solutions for initial value problems of nonlinear systems of second order integro-differential equations in Banach space.We improve and generalize some results (see[5,6]), and the results is new even in finite dimensional spaces.
Keywords: Systems of integro-differential equations, monotone iterative method, comparison result, cone.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14892526 Stepsize Control of the Finite Difference Method for Solving Ordinary Differential Equations
Authors: Davod Khojasteh Salkuyeh
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An important task in solving second order linear ordinary differential equations by the finite difference is to choose a suitable stepsize h. In this paper, by using the stochastic arithmetic, the CESTAC method and the CADNA library we present a procedure to estimate the optimal stepsize hopt, the stepsize which minimizes the global error consisting of truncation and round-off error.
Keywords: Ordinary differential equations, optimal stepsize, error, stochastic arithmetic, CESTAC, CADNA.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13532525 Improving Load Frequency Control of Multi-Area Power System by Considering Uncertainty by Using Optimized Type 2 Fuzzy Pid Controller with the Harmony Search Algorithm
Authors: Mehrdad Mahmudizad, Roya Ahmadi Ahangar
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This paper presents the method of designing the type 2 fuzzy PID controllers in order to solve the problem of Load Frequency Control (LFC). The Harmony Search (HS) algorithm is used to regulate the measurement factors and the effect of uncertainty of membership functions of Interval Type 2 Fuzzy Proportional Integral Differential (IT2FPID) controllers in order to reduce the frequency deviation resulted from the load oscillations. The simulation results implicitly show that the performance of the proposed IT2FPID LFC in terms of error, settling time and resistance against different load oscillations is more appropriate and preferred than PID and Type 1 Fuzzy Proportional Integral Differential (T1FPID) controllers.Keywords: Load Frequency Control, Fuzzy-PID controller, Type 2 fuzzy system, Harmony Search algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17182524 Analytical Solution for the Zakharov-Kuznetsov Equations by Differential Transform Method
Authors: Saeideh Hesam, Alireza Nazemi, Ahmad Haghbin
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This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.
Keywords: Zakharov-Kuznetsov equation, differential transform method, closed form solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19192523 Step Method for Solving Nonlinear Two Delays Differential Equation in Parkinson’s Disease
Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly
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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.
Keywords: Parkinson's disease, Step method, delay differential equation, simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7232522 An Accurate Computation of Block Hybrid Method for Solving Stiff Ordinary Differential Equations
Authors: A. M. Sagir
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In this paper, self-starting block hybrid method of order (5,5,5,5)T is proposed for the solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block method are tested on stiff ordinary differential equations, and the results obtained compared favorably with the exact solution.Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14722521 Bernstein-Galerkin Approach for Perturbed Constant-Coefficient Differential Equations, One-Dimensional Analysis
Authors: Diego Garijo
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A numerical approach for solving constant-coefficient differential equations whose solutions exhibit boundary layer structure is built by inserting Bernstein Partition of Unity into Galerkin variational weak form. Due to the reproduction capability of Bernstein basis, such implementation shows excellent accuracy at boundaries and is able to capture sharp gradients of the field variable by p-refinement using regular distributions of equi-spaced evaluation points. The approximation is subjected to convergence experimentation and a procedure to assemble the discrete equations without a background integration mesh is proposed.
Keywords: Bernstein polynomials, Galerkin, differential equation, boundary layer.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18322520 Solution of Nonlinear Second-Order Pantograph Equations via Differential Transformation Method
Authors: Nemat Abazari, Reza Abazari
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In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.
Keywords: Nonlinear multi-pantograph equation, delay differential equation, differential transformation method, proportional delay conditions, closed form solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25392519 Variational Iteration Method for Solving Systems of Linear Delay Differential Equations
Authors: Sara Barati, Karim Ivaz
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In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.
Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24662518 Constructing Distinct Kinds of Solutions for the Time-Dependent Coefficients Coupled Klein-Gordon-Schrödinger Equation
Authors: Anupma Bansal
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We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.
Keywords: Klein-Gordon-Schödinger Equation, Lie Classical Method, Exact Solutions
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 45202517 Modelling for Temperature Non-Isothermal Continuous Stirred Tank Reactor Using Fuzzy Logic
Authors: Nasser Mohamed Ramli, Mohamad Syafiq Mohamad
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Many types of controllers were applied on the continuous stirred tank reactor (CSTR) unit to control the temperature. In this research paper, Proportional-Integral-Derivative (PID) controller are compared with Fuzzy Logic controller for temperature control of CSTR. The control system for temperature non-isothermal of a CSTR will produce a stable response curve to its set point temperature. A mathematical model of a CSTR using the most general operating condition was developed through a set of differential equations into S-function using MATLAB. The reactor model and S-function are developed using m.file. After developing the S-function of CSTR model, User-Defined functions are used to link to SIMULINK file. Results that are obtained from simulation and temperature control were better when using Fuzzy logic control compared to PID control.
Keywords: CSTR, temperature, PID, fuzzy logic.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24702516 Synchronization for Impulsive Fuzzy Cohen-Grossberg Neural Networks with Time Delays under Noise Perturbation
Authors: Changzhao Li, Juan Zhang
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In this paper, we investigate a class of fuzzy Cohen- Grossberg neural networks with time delays and impulsive effects. By virtue of stochastic analysis, Halanay inequality for stochastic differential equations, we find sufficient conditions for the global exponential square-mean synchronization of the FCGNNs under noise perturbation. In particular, the traditional assumption on the differentiability of the time-varying delays is no longer needed. Finally, a numerical example is given to show the effectiveness of the results in this paper.
Keywords: Fuzzy Cohen-Grossberg neural networks (FCGNNs), complete synchronization, time delays, impulsive, noise perturbation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13322515 Development Partitioning Intervalwise Block Method for Solving Ordinary Differential Equations
Authors: K.H.Khairul Anuar, K.I.Othman, F.Ishak, Z.B.Ibrahim, Z.Majid
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Solving Ordinary Differential Equations (ODEs) by using Partitioning Block Intervalwise (PBI) technique is our aim in this paper. The PBI technique is based on Block Adams Method and Backward Differentiation Formula (BDF). Block Adams Method only use the simple iteration for solving while BDF requires Newtonlike iteration involving Jacobian matrix of ODEs which consumes a considerable amount of computational effort. Therefore, PBI is developed in order to reduce the cost of iteration within acceptable maximum errorKeywords: Adam Block Method, BDF, Ordinary Differential Equations, Partitioning Block Intervalwise
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16602514 Determination of Adequate Fuzzy Inequalities for their Usage in Fuzzy Query Languages
Authors: Marcel Shirvanian, Wolfram Lippe
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Although the usefulness of fuzzy databases has been pointed out in several works, they are not fully developed in numerous domains. A task that is mostly disregarded and which is the topic of this paper is the determination of suitable inequalities for fuzzy sets in fuzzy query languages. This paper examines which kinds of fuzzy inequalities exist at all. Afterwards, different procedures are presented that appear theoretically appropriate. By being applied to various examples, their strengths and weaknesses are revealed. Furthermore, an algorithm for an efficient computation of the selected fuzzy inequality is shown.Keywords: Fuzzy Databases, Fuzzy Inequalities, Fuzzy QueryLanguages, Fuzzy Ranking.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13412513 Intelligent Path Tracking Hybrid Fuzzy Controller for a Unicycle-Type Differential Drive Robot
Authors: Abdullah M. Almeshal, Mohammad R. Alenezi, Muhammad Moaz
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In this paper, we discuss the performance of applying hybrid spiral dynamic bacterial chemotaxis (HSDBC) optimisation algorithm on an intelligent controller for a differential drive robot. A unicycle class of differential drive robot is utilised to serve as a basis application to evaluate the performance of the HSDBC algorithm. A hybrid fuzzy logic controller is developed and implemented for the unicycle robot to follow a predefined trajectory. Trajectories of various frictional profiles and levels were simulated to evaluate the performance of the robot at different operating conditions. Controller gains and scaling factors were optimised using HSDBC and the performance is evaluated in comparison to previously adopted optimisation algorithms. The HSDBC has proven its feasibility in achieving a faster convergence toward the optimal gains and resulted in a superior performance.
Keywords: Differential drive robot, hybrid fuzzy controller, optimization, path tracking, unicycle robot.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26202512 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 10102511 A Family of Zero Stable Block Integrator for the Solutions of Ordinary Differential Equations
Authors: A. M. Sagir
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In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different four discrete schemes, each of order (5,5,5,5)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block methods are tested on linear and non-linear ordinary differential equations and the results obtained compared favorably with the exact solution.Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14702510 On Symmetries and Exact Solutions of Einstein Vacuum Equations for Axially Symmetric Gravitational Fields
Authors: Nisha Goyal, R.K. Gupta
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Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained.Keywords: Gravitational fields, Lie Classical method, Exact solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19252509 Numerical Investigation of Two-dimensional Boundary Layer Flow Over a Moving Surface
Authors: Mahmoud Zarrini, R.N. Pralhad
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In this chapter, we have studied Variation of velocity in incompressible fluid over a moving surface. The boundary layer equations are on a fixed or continuously moving flat plate in the same or opposite direction to the free stream with suction and injection. The boundary layer equations are transferred from partial differential equations to ordinary differential equations. Numerical solutions are obtained by using Runge-Kutta and Shooting methods. We have found numerical solution to velocity and skin friction coefficient.
Keywords: Boundary layer, continuously moving surface, shooting method, skin friction coefficient.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15682508 Comparing the Efficiency of Simpson’s 1/3 and 3/8 Rules for the Numerical Solution of First Order Volterra Integro-Differential Equations
Authors: N. M. Kamoh, D. G. Gyemang, M. C. Soomiyol
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This paper compared the efficiency of Simpson’s 1/3 and 3/8 rules for the numerical solution of first order Volterra integro-differential equations. In developing the solution, collocation approximation method was adopted using the shifted Legendre polynomial as basis function. A block method approach is preferred to the predictor corrector method for being self-starting. Experimental results confirmed that the Simpson’s 3/8 rule is more efficient than the Simpson’s 1/3 rule.
Keywords: Collocation shifted Legendre polynomials, Simpson’s rule and Volterra integro-differential equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9652507 Stabilization of the Lorenz Chaotic Equations by Fuzzy Controller
Authors: Behrooz Rezaie, Zahra Rahmani Cherati, Mohammad Reza Jahed Motlagh, Mohammad Farrokhi
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In this paper, a fuzzy controller is designed for stabilization of the Lorenz chaotic equations. A simple Mamdani inference method is used for this purpose. This method is very simple and applicable for complex chaotic systems and it can be implemented easily. The stability of close loop system is investigated by the Lyapunov stabilization criterion. A Lyapunov function is introduced and the global stability is proven. Finally, the effectiveness of this method is illustrated by simulation results and it is shown that the performance of the system is improved.Keywords: Chaotic system, Fuzzy control, Lorenz equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20142506 Intuitionistic Fuzzy Points in Semigroups
Authors: Sujit Kumar Sardar Manasi Mandal Samit Kumar Majumder
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The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. Y.B. Jun and S.Z. Song introduced the notion of intuitionistic fuzzy points. In this paper we find some relations between the intuitionistic fuzzy ideals of a semigroup S and the set of all intuitionistic fuzzy points of S.Keywords: Semigroup, Regular(intra-regular) semigroup, Intuitionistic fuzzy point, Intuitionistic fuzzy subsemigroup, Intuitionistic fuzzy ideal, Intuitionistic fuzzy interior ideal, Intuitionistic fuzzy semiprime ideal, Intuitionistic fuzzy prime ideal.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18342505 Noise Analysis of Single-Ended Input Differential Amplifier using Stochastic Differential Equation
Authors: Tarun Kumar Rawat, Abhirup Lahiri, Ashish Gupta
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In this paper, we analyze the effect of noise in a single- ended input differential amplifier working at high frequencies. Both extrinsic and intrinsic noise are analyzed using time domain method employing techniques from stochastic calculus. Stochastic differential equations are used to obtain autocorrelation functions of the output noise voltage and other solution statistics like mean and variance. The analysis leads to important design implications and suggests changes in the device parameters for improved noise characteristics of the differential amplifier.
Keywords: Single-ended input differential amplifier, Noise, stochastic differential equation, mean and variance.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16962504 On The Comparison of Fuzzy Logic and State Space Averaging based Sliding Control Methods Applied onan Arc Welding Machine
Authors: İres İskender, Ahmet Karaarslan
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In this study, the performance of a high-frequency arc welding machine including a two-switch inverter is analyzed. The control of the system is achieved using two different control techniques i- fuzzy logic control (FLC) ii- state space averaging based sliding control. Fuzzy logic control does not need accurate mathematical model of a plant and can be used in nonlinear applications. The second method needs the mathematical model of the system. In this method the state space equations of the system are derived for two different “on" and “off" states of the switches. The derived state equations are combined with the sliding control rule considering the duty-cycle of the converter. The performance of the system is analyzed by simulating the system using SIMULINK tool box of MATLAB. The simulation results show that fuzzy logic controller is more robust and less sensitive to parameter variations.Keywords: Fuzzy logic, arc welding, sliding state space control, PWM, current control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20432503 Blow up in Polynomial Differential Equations
Authors: Rudolf Csikja, Janos Toth
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Methods to detect and localize time singularities of polynomial and quasi-polynomial ordinary differential equations are systematically presented and developed. They are applied to examples taken form different fields of applications and they are also compared to better known methods such as those based on the existence of linear first integrals or Lyapunov functions.
Keywords: blow up, finite escape time, polynomial ODE, singularity, Lotka–Volterra equation, Painleve analysis, Ψ-series, global existence
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