Search results for: fully differential transconductor
1038 An Analytical Method for Solving General Riccati Equation
Authors: Y. Pala, M. O. Ertas
Abstract:
In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.
Keywords: Riccati Equation, ordinary differential equation, nonlinear differential equation, analytical solution, proper solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20091037 Ordinary Differential Equations with Inverted Functions
Authors: Thomas Kampke
Abstract:
Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.
Keywords: Euler method, fixed points, golden section, multi-step procedures, Runge Kutta methods.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14341036 A Fully Parallel Reverse Converter
Authors: Mehdi Hosseinzadeh, Amir Sabbagh Molahosseini, Keivan Navi
Abstract:
The residue number system (RNS) is popular in high performance computation applications because of its carry-free nature. The challenges of RNS systems design lie in the moduli set selection and in the reverse conversion from residue representation to weighted representation. In this paper, we proposed a fully parallel reverse conversion algorithm for the moduli set {rn - 2, rn - 1, rn}, based on simple mathematical relationships. Also an efficient hardware realization of this algorithm is presented. Our proposed converter is very faster and results to hardware savings, compared to the other reverse converters.Keywords: Reverse converter, residue to weighted converter, residue number system, multiple-valued logic, computer arithmetic.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15731035 Controller Design of Discrete Systems by Order Reduction Technique Employing Differential Evolution Optimization Algorithm
Authors: J. S. Yadav, N. P. Patidar, J. Singhai
Abstract:
One of the main objectives of order reduction is to design a controller of lower order which can effectively control the original high order system so that the overall system is of lower order and easy to understand. In this paper, a simple method is presented for controller design of a higher order discrete system. First the original higher order discrete system in reduced to a lower order model. Then a Proportional Integral Derivative (PID) controller is designed for lower order model. An error minimization technique is employed for both order reduction and controller design. For the error minimization purpose, Differential Evolution (DE) optimization algorithm has been employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the desired response and actual response pertaining to a unit step input. Finally the designed PID controller is connected to the original higher order discrete system to get the desired specification. The validity of the proposed method is illustrated through a numerical example.Keywords: Discrete System, Model Order Reduction, PIDController, Integral Squared Error, Differential Evolution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18861034 Investigating the Dynamics of Knowledge Acquisition in Learning Using Differential Equations
Authors: Gilbert Makanda, Roelf Sypkens
Abstract:
A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.Keywords: Differential equations, knowledge acquisition, least squares nonlinear, dynamical systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9021033 A PWM Controller with Multiple-Access Table Look-up for DC-DC Buck Conversion
Authors: Steve Hung-Lung Tu, Chu-Tse Lee
Abstract:
A new power regulator controller with multiple-access PID compensator is proposed, which can achieve a minimum memory requirement for fully table look-up. The proposed regulator controller employs hysteresis comparators, an error process unit (EPU) for voltage regulation, a multiple-access PID compensator and a lowpower- consumption digital PWM (DPWM). Based on the multipleaccess mechanism, the proposed controller can alleviate the penalty of large amount of memory employed for fully table look-up based PID compensator in the applications of power regulation. The proposed controller has been validated with simulation results.Keywords: Multiple access, PID compensator, PWM, Buck conversion.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14281032 Seven step Adams Type Block Method With Continuous Coefficient For Periodic Ordinary Differential Equation
Authors: Olusheye Akinfenwa
Abstract:
We consider the development of an eight order Adam-s type method, with A-stability property discussed by expressing them as a one-step method in higher dimension. This makes it suitable for solving variety of initial-value problems. The main method and additional methods are obtained from the same continuous scheme derived via interpolation and collocation procedures. The methods are then applied in block form as simultaneous numerical integrators over non-overlapping intervals. Numerical results obtained using the proposed block form reveals that it is highly competitive with existing methods in the literature.Keywords: Block Adam's type Method; Periodic Ordinary Differential Equation; Stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15711031 Transformer Life Enhancement Using Dynamic Switching of Second Harmonic Feature in IEDs
Authors: K. N. Dinesh Babu, P. K. Gargava
Abstract:
Energization of a transformer results in sudden flow of current which is an effect of core magnetization. This current will be dominated by the presence of second harmonic, which in turn is used to segregate fault and inrush current, thus guaranteeing proper operation of the relay. This additional security in the relay sometimes obstructs or delays differential protection in a specific scenario, when the 2nd harmonic content was present during a genuine fault. This kind of scenario can result in isolation of the transformer by Buchholz and pressure release valve (PRV) protection, which is acted when fault creates more damage in transformer. Such delays involve a huge impact on the insulation failure, and chances of repairing or rectifying fault of problem at site become very dismal. Sometimes this delay can cause fire in the transformer, and this situation becomes havoc for a sub-station. Such occurrences have been observed in field also when differential relay operation was delayed by 10-15 ms by second harmonic blocking in some specific conditions. These incidences have led to the need for an alternative solution to eradicate such unwarranted delay in operation in future. Modern numerical relay, called as intelligent electronic device (IED), is embedded with advanced protection features which permit higher flexibility and better provisions for tuning of protection logic and settings. Such flexibility in transformer protection IEDs, enables incorporation of alternative methods such as dynamic switching of second harmonic feature for blocking the differential protection with additional security. The analysis and precautionary measures carried out in this case, have been simulated and discussed in this paper to ensure that similar solutions can be adopted to inhibit analogous issues in future.
Keywords: Differential protection, intelligent electronic device (IED), 2nd harmonic, inrush inhibit.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10361030 A Hyperexponential Approximation to Finite-Time and Infinite-Time Ruin Probabilities of Compound Poisson Processes
Authors: Amir T. Payandeh Najafabadi
Abstract:
This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equation). Application of our findings has been given through a simulation study.Keywords: Ruin probability, compound Poisson processes, mixture exponential (hyperexponential) distribution, heavy-tailed distributions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12721029 Optimized Vector Quantization for Bayer Color Filter Array
Authors: M. Lakshmi, J. Senthil Kumar
Abstract:
Digital cameras to reduce cost, use an image sensor to capture color images. Color Filter Array (CFA) in digital cameras permits only one of the three primary (red-green-blue) colors to be sensed in a pixel and interpolates the two missing components through a method named demosaicking. Captured data is interpolated into a full color image and compressed in applications. Color interpolation before compression leads to data redundancy. This paper proposes a new Vector Quantization (VQ) technique to construct a VQ codebook with Differential Evolution (DE) Algorithm. The new technique is compared to conventional Linde- Buzo-Gray (LBG) method.Keywords: Color Filter Array (CFA), Biorthogonal Wavelet, Vector Quantization (VQ), Differential Evolution (DE).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19001028 Stability of Fractional Differential Equation
Authors: Rabha W. Ibrahim
Abstract:
We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.
Keywords: Fractional calculus, fractional differential equation, Lane-Emden equation, Riemann-Liouville fractional operators, Volterra integral equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 37001027 Solving the Economic Dispatch Problem using Novel Particle Swarm Optimization
Authors: S. Khamsawang, S. Jiriwibhakorn
Abstract:
This paper proposes an improved approach based on conventional particle swarm optimization (PSO) for solving an economic dispatch(ED) problem with considering the generator constraints. The mutation operators of the differential evolution (DE) are used for improving diversity exploration of PSO, which called particle swarm optimization with mutation operators (PSOM). The mutation operators are activated if velocity values of PSO nearly to zero or violated from the boundaries. Four scenarios of mutation operators are implemented for PSOM. The simulation results of all scenarios of the PSOM outperform over the PSO and other existing approaches which appeared in literatures.Keywords: Novel particle swarm optimization, Economic dispatch problem, Mutation operator, Prohibited operating zones, Differential Evolution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23011026 RBF- based Meshless Method for Free Vibration Analysis of Laminated Composite Plates
Authors: Jeeoot Singh, Sandeep Singh, K. K. Shukla
Abstract:
The governing differential equations of laminated plate utilizing trigonometric shear deformation theory are derived using energy approach. The governing differential equations discretized by different radial basis functions are used to predict the free vibration behavior of symmetric laminated composite plates. Effect of orthotropy and span to thickness ratio on frequency parameter of simply supported laminated plate is presented. Numerical results show the accuracy and good convergence of radial basis functions.Keywords: Composite plates, Meshfree method, free vibration, Shear deformation, RBFs
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21151025 Seismic Performance of Reinforced Concrete Frames Infilled by Masonry Walls with Different Heights
Authors: Ji–Wook Mauk, Yu–Suk Kim, Hyung–Joon Kim
Abstract:
This study carried out comparative seismic performance of reinforced concrete frames infilled by masonry walls with different heights. Partial and fully infilled reinforced concrete frames were modeled for the research objectives and the analysis model for a bare reinforced concrete frame was also established for comparison. Non–linear static analyses for the studied frames were performed to investigate their structural behavior under extreme seismic loads and to find out their collapse mechanism. It was observed from analysis results that the strengths of the partial infilled reinforced concrete frames are increased and their ductilities are reduced, as infilled masonry walls are higher. Especially, reinforced concrete frames with higher partial infilled masonry walls would experience shear failures. Non–linear dynamic analyses using 10 earthquake records show that the bare and fully infilled reinforced concrete frame present stable collapse mechanism while the reinforced concrete frames with partially infilled masonry walls collapse in more brittle manner due to short-column effects.
Keywords: Fully infilled RC frame, partially infilled RC frame, masonry wall, short–column effects.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25831024 A New Solution for Natural Convection of Darcian Fluid about a Vertical Full Cone Embedded in Porous Media Prescribed Wall Temperature by using a Hybrid Neural Network-Particle Swarm Optimization Method
Authors: M.A.Behrang, M. Ghalambaz, E. Assareh, A.R. Noghrehabadi
Abstract:
Fluid flow and heat transfer of vertical full cone embedded in porous media is studied in this paper. Nonlinear differential equation arising from similarity solution of inverted cone (subjected to wall temperature boundary conditions) embedded in porous medium is solved using a hybrid neural network- particle swarm optimization method. To aim this purpose, a trial solution of the differential equation is defined as sum of two parts. The first part satisfies the initial/ boundary conditions and does contain an adjustable parameter and the second part which is constructed so as not to affect the initial/boundary conditions and involves adjustable parameters (the weights and biases) for a multi-layer perceptron neural network. Particle swarm optimization (PSO) is applied to find adjustable parameters of trial solution (in first and second part). The obtained solution in comparison with the numerical ones represents a remarkable accuracy.Keywords: Porous Media, Ordinary Differential Equations (ODE), Particle Swarm Optimization (PSO), Neural Network (NN).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17061023 Molecular Dynamics Simulation for Buckling Analysis at Nanocomposite Beams
Authors: Babak Safaei, A. M. Fattahi
Abstract:
In the present study we have investigated axial buckling characteristics of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs). Various types of beam theories including Euler-Bernoulli beam theory, Timoshenko beam theory and Reddy beam theory were used to analyze the buckling behavior of carbon nanotube-reinforced composite beams. Generalized differential quadrature (GDQ) method was utilized to discretize the governing differential equations along with four commonly used boundary conditions. The material properties of the nanocomposite beams were obtained using molecular dynamic (MD) simulation corresponding to both short-(10,10) SWCNT and long- (10,10) SWCNT composites which were embedded by amorphous polyethylene matrix. Then the results obtained directly from MD simulations were matched with those calculated by the mixture rule to extract appropriate values of carbon nanotube efficiency parameters accounting for the scale-dependent material properties. The selected numerical results were presented to indicate the influences of nanotube volume fractions and end supports on the critical axial buckling loads of nanocomposite beams relevant to long- and short-nanotube composites.Keywords: Nanocomposites, molecular dynamics simulation, axial buckling, generalized differential quadrature (GDQ).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18921022 An Automated High Pressure Differential Thermal Analysis System for Phase Transformation Studies
Authors: T. K. Mondal, N C Shivaprakash
Abstract:
A piston cylinder based high pressure differential thermal analyzer system is developed to investigate phase transformations, melting, glass transitions, crystallization behavior of inorganic materials, glassy systems etc., at ambient to 4 GPa and at room temperature to 1073 K. The pressure is calibrated by the phase transition of bismuth and ytterbium and temperature is calibrated by using thermocouple data chart. The system developed is calibrated using benzoic acid, ammonium nitrate and it has a pressure and temperature control of ± 8.9 x 10 -4 GPa , ± 2 K respectively. The phase transition of Asx Te100-x chalcogenides, ferrous oxide and strontium boride are studied using the indigenously developed system.Keywords: double stage crystallization, Phase transition, Quasi hydrostatic, Rigidity percolation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16761021 Dual Solutions in Mixed Convection Boundary Layer Flow: A Stability Analysis
Authors: Anuar Ishak
Abstract:
The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.
Keywords: Dual solutions, heat transfer, mixed convection, stability analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24701020 An Analytical Method to Analysis of Foam Drainage Problem
Authors: A. Nikkar, M. Mighani
Abstract:
In this study, a new reliable technique use to handle the foam drainage equation. This new method is resulted from VIM by a simple modification that is Reconstruction of Variational Iteration Method (RVIM). The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. Results are compared with those of Adomian’s decomposition method (ADM).The comparisons show that the Reconstruction of Variational Iteration Method is very effective and overcome the difficulty of traditional methods and quite accurate to systems of non-linear partial differential equations.
Keywords: Reconstruction of Variational Iteration Method (RVIM), Foam drainage, nonlinear partial differential equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18031019 Numerical Simulation of unsteady MHD Flow and Heat Transfer of a Second Grade Fluid with Viscous Dissipation and Joule Heating using Meshfree Approach
Authors: R. Bhargava, Sonam Singh
Abstract:
In the present study, a numerical analysis is carried out to investigate unsteady MHD (magneto-hydrodynamic) flow and heat transfer of a non-Newtonian second grade viscoelastic fluid over an oscillatory stretching sheet. The flow is induced due to an infinite elastic sheet which is stretched oscillatory (back and forth) in its own plane. Effect of viscous dissipation and joule heating are taken into account. The non-linear differential equations governing the problem are transformed into system of non-dimensional differential equations using similarity transformations. A newly developed meshfree numerical technique Element free Galerkin method (EFGM) is employed to solve the coupled non linear differential equations. The results illustrating the effect of various parameters like viscoelastic parameter, Hartman number, relative frequency amplitude of the oscillatory sheet to the stretching rate and Eckert number on velocity and temperature field are reported in terms of graphs and tables. The present model finds its application in polymer extrusion, drawing of plastic films and wires, glass, fiber and paper production etc.Keywords: EFGM, MHD, Oscillatory stretching sheet, Unsteady, Viscoelastic
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18831018 Implicit Two Step Continuous Hybrid Block Methods with Four Off-Steps Points for Solving Stiff Ordinary Differential Equation
Authors: O. A. Akinfenwa, N.M. Yao, S. N. Jator
Abstract:
In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Off-step points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the stiff ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.Keywords: Collocation and Interpolation, Continuous HybridBlock Formulae, Off-Step Points, Stability, Stiff ODEs.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20911017 Power System Stability Improvement by Simultaneous Tuning of PSS and SVC Based Damping Controllers Employing Differential Evolution Algorithm
Authors: Sangram Keshori Mohapatra, Sidhartha Panda, Prasant Kumar Satpathy
Abstract:
Power-system stability improvement by simultaneous tuning of power system stabilizer (PSS) and a Static Var Compensator (SVC) based damping controller is thoroughly investigated in this paper. Both local and remote signals with associated time delays are considered in the present study. The design problem of the proposed controller is formulated as an optimization problem, and differential evolution (DE) algorithm is employed to search for the optimal controller parameters. The performances of the proposed controllers are evaluated under different disturbances for both single-machine infinite bus power system and multi-machine power system. The performance of the proposed controllers with variations in the signal transmission delays has also been investigated. The proposed stabilizers are tested on a weakly connected power system subjected to different disturbances. Nonlinear simulation results are presented to show the effectiveness and robustness of the proposed control schemes over a wide range of loading conditions and disturbances. Further, the proposed design approach is found to be robust and improves stability effectively even under small disturbance conditions.
Keywords: Differential Evolution Algorithm, Power System Stability, Power System Stabilizer, Static Var Compensator
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23301016 Parallel Particle Swarm Optimization Optimized LDI Controller with Lyapunov Stability Criterion for Nonlinear Structural Systems
Authors: P.-W. Tsai, W.-L. Hong, C.-W. Chen, C.-Y. Chen
Abstract:
In this paper, we present a neural-network (NN) based approach to represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.
Keywords: Lyapunov Stability, Parallel Particle Swarm Optimization, Linear Differential Inclusion, Artificial Intelligence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18531015 Phosphorus Reduction in Plain and Fully Formulated Oils Using Fluorinated Additives
Authors: Gabi N. Nehme
Abstract:
The reduction of phosphorus and sulfur in engine oil are the main topics of this paper. Very reproducible boundary lubrication tests were conducted as part of Design of Experiment software (DOE) to study the behavior of fluorinated catalyst iron fluoride (FeF3), and polutetrafluoroethylene or Teflon (PTFE) in developing environmentally friendly (reduced P and S) anti-wear additives for future engine oil formulations. Multi-component Chevron fully formulated oil (GF3) and Chevron plain oil were used with the addition of PTFE and catalyst to characterize and analyze their performance. Lower phosphorus blends were the goal of the model solution. Experiments indicated that new sub-micron FeF3 catalyst played an important role in preventing breakdown of the tribofilm.Keywords: Wear, SEM, EDS, friction, lubricants.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19791014 Effect of Thermal Radiation on Temperature Variation in 2-D Stagnation-Point flow
Authors: Vai Kuong Sin
Abstract:
Non-isothermal stagnation-point flow with consideration of thermal radiation is studied numerically. A set of partial differential equations that governing the fluid flow and energy is converted into a set of ordinary differential equations which is solved by Runge-Kutta method with shooting algorithm. Dimensionless wall temperature gradient and temperature boundary layer thickness for different combinaton of values of Prandtl number Pr and radiation parameter NR are presented graphically. Analyses of results show that the presence of thermal radiation in the stagnation-point flow is to increase the temperature boundary layer thickness and decrease the dimensionless wall temperature gradient.
Keywords: Stagnation-point flow, Similarity solution, Thermal radiation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15241013 Basket Option Pricing under Jump Diffusion Models
Authors: Ali Safdari-Vaighani
Abstract:
Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. The option pricing under asset price involving jump diffusion processes leads to the partial integral differential equation (PIDEs), which is an extension of the Black-Scholes PDE with a new integral term. The aim of this paper is to show how basket option prices in the jump diffusion models, mainly on the Merton model, can be computed using RBF based approximation methods. For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. The numerical result shows the accuracy and efficiency of the presented method.Keywords: Radial basis function, basket option, jump diffusion, RBF-PUM.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12011012 The Dividend Payments for General Claim Size Distributions under Interest Rate
Authors: Li-Li Li, Jinghai Feng, Lixin Song
Abstract:
This paper evaluates the dividend payments for general claim size distributions in the presence of a dividend barrier. The surplus of a company is modeled using the classical risk process perturbed by diffusion, and in addition, it is assumed to accrue interest at a constant rate. After presenting the integro-differential equation with initial conditions that dividend payments satisfies, the paper derives a useful expression of the dividend payments by employing the theory of Volterra equation. Furthermore, the optimal value of dividend barrier is found. Finally, numerical examples illustrate the optimality of optimal dividend barrier and the effects of parameters on dividend payments.Keywords: Dividend payout, Integro-differential equation, Jumpdiffusion model, Volterra equation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17861011 Some Solitary Wave Solutions of Generalized Pochhammer-Chree Equation via Exp-function Method
Authors: Kourosh Parand, Jamal Amani Rad
Abstract:
In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that the Exp-function method is direct, effective, succinct and can be used for many other nonlinear partial differential equations.
Keywords: Exp-function method, generalized Pochhammer- Chree equation, solitary wave solution, ODE's.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15801010 On Symmetries and Exact Solutions of Einstein Vacuum Equations for Axially Symmetric Gravitational Fields
Authors: Nisha Goyal, R.K. Gupta
Abstract:
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 19251009 Offset Dependent Uniform Delay Mathematical Optimization Model for Signalized Traffic Network Using Differential Evolution Algorithm
Authors: Tahseen Al-Shaikhli, Halim Ceylan, Jonathan Weaver, Osman Nuri Çelik, Onur Gungor Sahin
Abstract:
A concept of uniform delay offset dependent mathematical optimization problem is derived as the main objective for this study using a differential evolution algorithm. Furthermore, the objectives are to control the coordination problem which mainly depends on offset selection, and to estimate the uniform delay based on the offset choice at each signalized intersection. The assumption is the periodic sinusoidal function for arrival and departure patterns. The cycle time is optimized at the entry links and the optimized value is used in the non-entry links as a common cycle time. The offset optimization algorithm is used to calculate the uniform delay at each link. The results are illustrated by using a case study and compared with the canonical uniform delay model derived by Webster and the highway capacity manual’s model. The findings show that the derived model minimizes the total uniform delay to almost half compared to conventional models; the mathematical objective function is robust; the algorithm convergence time is fast.
Keywords: Area traffic control, differential evolution, offset variable, sinusoidal periodic function, traffic flow, uniform delay.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 336