Search results for: differential rectifier
1651 High Precision 65nm CMOS Rectifier for Energy Harvesting using Threshold Voltage Minimization in Telemedicine Embedded System
Authors: Hafez Fouad
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Telemedicine applications have very low voltage which required High Precision Rectifier Design with high Sensitivity to operate at minimum input Voltage. In this work, we targeted 0.2V input voltage using 65 nm CMOS rectifier for Energy Harvesting Telemedicine application. The proposed rectifier which designed at 2.4GHz using two-stage structure found to perform in a better case where minimum operation voltage is lower than previous published paper and the rectifier can work at a wide range of low input voltage amplitude. The Performance Summary of Full-wave fully gate cross-coupled rectifiers (FWFR) CMOS Rectifier at F = 2.4 GHz: The minimum and maximum output voltages generated using an input voltage amplitude of 2 V are 490.9 mV and 1.997 V, maximum VCE = 99.85 % and maximum PCE = 46.86 %. The Performance Summary of Differential drive CMOS rectifier with external bootstrapping circuit rectifier at F = 2.4 GHz: The minimum and maximum output voltages generated using an input voltage amplitude of 2V are 265.5 mV (0.265V) and 1.467 V respectively, maximum VCE = 93.9 % and maximum PCE= 15.8 %.Keywords: energy harvesting, embedded system, IoT telemedicine system, threshold voltage minimization, differential drive cmos rectifier, full-wave fully gate cross-coupled rectifiers CMOS rectifier
Procedia PDF Downloads 1311650 Bridgeless Boost Power Factor Correction Rectifier with Hold-Up Time Extension Circuit
Authors: Chih-Chiang Hua, Yi-Hsiung Fang, Yuan-Jhen Siao
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A bridgeless boost (BLB) power factor correction (PFC) rectifier with hold-up time extension circuit is proposed in this paper. A full bridge rectifier is widely used in the front end of the ac/dc converter. Since the shortcomings of the full bridge rectifier, the bridgeless rectifier is developed. A BLB rectifier topology is utilized with the hold-up time extension circuit. Unlike the traditional hold-up time extension circuit, the proposed extension scheme uses fewer active switches to achieve a longer hold-up time. Simulation results are presented to verify the converter performance.Keywords: bridgeless boost (BLB), boost converter, power factor correction (PFC), hold-up time
Procedia PDF Downloads 3951649 Design of a Rectifier with Enhanced Efficiency and a High-gain Antenna for Integrated and Compact-size Rectenna Circuit
Authors: Rawaa Maher, Ahmed Allam, Haruichi Kanaya, Adel B. Abdelrahman
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In this paper, a compact, high-efficiency integrated rectenna is presented to operate in the 2.45 GHz band. A comparison between two rectifier topologies is performed to verify the benefits of removing the matching network from the rectifier. A rectifier high conversion efficiency of 74.1% is achieved. To complete the rectenna system, a novel omnidirectional antenna with high gain (3.72 dB) and compact size (25 mm * 29 mm) is designed and fabricated. The same antenna is used with a reflector for raising the gain to nearly 8.3 dB. The simulation and measurement results of the antenna are in good agreement.Keywords: internet of things, integrated rectenna, rectenna, RF energy harvesting, wireless sensor networks(WSN)
Procedia PDF Downloads 1591648 Analysis and Design of Simultaneous Dual Band Harvesting System with Enhanced Efficiency
Authors: Zina Saheb, Ezz El-Masry, Jean-François Bousquet
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This paper presents an enhanced efficiency simultaneous dual band energy harvesting system for wireless body area network. A bulk biasing is used to enhance the efficiency of the adapted rectifier design to reduce Vth of MOSFET. The presented circuit harvests the radio frequency (RF) energy from two frequency bands: 1 GHz and 2.4 GHz. It is designed with TSMC 65-nm CMOS technology and high quality factor dual matching network to boost the input voltage. Full circuit analysis and modeling is demonstrated. The simulation results demonstrate a harvester with an efficiency of 23% at 1 GHz and 46% at 2.4 GHz at an input power as low as -30 dBm.Keywords: energy harvester, simultaneous, dual band, CMOS, differential rectifier, voltage boosting, TSMC 65nm
Procedia PDF Downloads 3871647 A Strategy of Direct Power Control for PWM Rectifier Reducing Ripple in Instantaneous Power
Authors: T. Mohammed Chikouche, K. Hartani
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In order to solve the instantaneous power ripple and achieve better performance of direct power control (DPC) for a three-phase PWM rectifier, a control method is proposed in this paper. This control method is applied to overcome the instantaneous power ripple, to eliminate line current harmonics and therefore reduce the total harmonic distortion and to improve the power factor. A switching table is based on the analysis on the change of instantaneous active and reactive power, to select the optimum switching state of the three-phase PWM rectifier. The simulation result shows feasibility of this control method.Keywords: power quality, direct power control, power ripple, switching table, unity power factor
Procedia PDF Downloads 3001646 Low Trigger Voltage Silicon Controlled Rectifier Stacking Structure with High Holding Voltage for High Voltage Applications
Authors: Kyoung-Il Do, Jun-Geol Park, Hee-Guk Chae, Jeong-Yun Seo, Yong-Seo Koo
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A SCR stacking structure is proposed to have improved Latch-up immunity. In comparison with conventional SCR (Silicon Controlled Rectifier), the proposed Electrostatic Discharge (ESD) protection circuit has a lower trigger characteristic by using the LVTSCR (Low Voltage Trigger) structure. Also the proposed ESD protection circuit has improved Holding Voltage Characteristic by using N-stack technique. These characteristics enable to have latch-up immunity in operating conditions. The simulations are accomplished by using the Synopsys TCAD. It has a trigger voltage of 8.9V and a holding voltage of 1.8V in a single structure. And when applying the stack technique, 2-stack has the holding voltage of 3.8V and 3-stack has the holding voltage of 5.1 V.Keywords: electrostatic discharge (ESD), low voltage trigger silicon controlled rectifier (LVTSCR), MVTSCR, power clamp, silicon controlled rectifier (SCR), latch-up
Procedia PDF Downloads 4271645 Analysis of a Power Factor Correction Converter for Light Emitting Diode Driver Application
Authors: Edwina G. Rodrigues, S. J. Bindhu, A. V. Rajesh
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This paper proposes a switched capacitor based driver circuit for high power light emitting diodes with a front end rectifier. LEDs are low-voltage light sources, requiring a constant DC voltage or current to operate optimally. LEDs, therefore, require a device that can convert incoming AC power to the proper DC voltage, and regulate the current flowing through the LED during operation. Proposed topology has a front end converter. It is an AC-DC rectifier that works on bridgeless boost topology which shapes the input current waveform. The front end converter is followed by a DC-DC converter which provides a constant DC voltage across the LEDs. A 12V AC input is given to the input of frontend converter which rectifies and boost the voltage to 24v DC and gives it to the DC-DC converter. The DC-DC converter converts the 24V DC and regulates this constant DC voltage across the LEDs.Keywords: bridgeless rectifier, power factor correction(PFC), SC converter, total harmonic distortion (THD)
Procedia PDF Downloads 8551644 Noncommutative Differential Structure on Finite Groups
Authors: Ibtisam Masmali, Edwin Beggs
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In this paper, we take example of differential calculi, on the finite group A4. Then, we apply methods of non-commutative of non-commutative differential geometry to this example, and see how similar the results are to those of classical differential geometry.Keywords: differential calculi, finite group A4, Christoffel symbols, covariant derivative, torsion compatible
Procedia PDF Downloads 2301643 Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations
Authors: Fuziyah Ishak, Siti Norazura Ahmad
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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations
Procedia PDF Downloads 4021642 Analysis of SCR-Based ESD Protection Circuit on Holding Voltage Characteristics
Authors: Yong Seo Koo, Jong Ho Nam, Yong Nam Choi, Dae Yeol Yoo, Jung Woo Han
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This paper presents a silicon controller rectifier (SCR) based ESD protection circuit for IC. The proposed ESD protection circuit has low trigger voltage and high holding voltage compared with conventional SCR ESD protection circuit. Electrical characteristics of the proposed ESD protection circuit are simulated and analyzed using TCAD simulator. The proposed ESD protection circuit verified effective low voltage ESD characteristics with low trigger voltage and high holding voltage.Keywords: electro-static discharge (ESD), silicon controlled rectifier (SCR), holding voltage, protection circuit
Procedia PDF Downloads 3581641 Performance Analysis of a 6-Phase PMG Exciter with Rotating Thyristor-Controlled Rectification Topologies
Authors: Jonas Kristiansen Nøland, Karina Hjelmervik, Urban Lundin
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The thyristor bridge rectifier is often used for control of excitation equipment for synchronous generators. However, on the rotating shaft of brushless exciters, the diode bridge rectifier is mostly used. The step response of a conventional brushless rotating excitation system is slow compared to static excitation systems. This paper investigates the performance of different thyristor-controlled rectification topologies applied on the shaft of a 6-phase PMG exciter connected to a synchronous generator. One of the important issues is the steady-state torque ripple produced by the thyristor bridges.Keywords: brushless exciters, rotating exciters, permanent magnet machines, synchronous generators
Procedia PDF Downloads 4581640 Existence Result of Third Order Functional Random Integro-Differential Inclusion
Authors: D. S. Palimkar
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The FRIGDI (functional random integrodifferential inclusion) seems to be new and includes several known random differential inclusions already studied in the literature as special cases have been discussed in the literature for various aspects of the solutions. In this paper, we prove the existence result for FIGDI under the non-convex case of multi-valued function involved in it.Using random fixed point theorem of B. C. Dhage and caratheodory condition. This result is new to the theory of differential inclusion.Keywords: caratheodory condition, random differential inclusion, random solution, integro-differential inclusion
Procedia PDF Downloads 4481639 A Silicon Controlled Rectifier-Based ESD Protection Circuit with High Holding Voltage and High Robustness Characteristics
Authors: Kyoung-il Do, Byung-seok Lee, Hee-guk Chae, Jeong-yun Seo Yong-seo Koo
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In this paper, a Silicon Controlled Rectifier (SCR)-based Electrostatic Discharge (ESD) protection circuit with high holding voltage and high robustness characteristics is proposed. Unlike conventional SCR, the proposed circuit has low trigger voltage and high holding voltage and provides effective ESD protection with latch-up immunity. In addition, the TCAD simulation results show that the proposed circuit has better electrical characteristics than the conventional SCR. A stack technology was used for voltage-specific applications. Consequentially, the proposed circuit has a trigger voltage of 17.60 V and a holding voltage of 3.64 V.Keywords: ESD, SCR, latch-up, power clamp, holding voltage
Procedia PDF Downloads 3831638 An Active Rectifier with Time-Domain Delay Compensation to Enhance the Power Conversion Efficiency
Authors: Shao-Ku Kao
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This paper presents an active rectifier with time-domain delay compensation to enhance the efficiency. A delay calibration circuit is designed to convert delay time to voltage and adaptive control on/off delay in variable input voltage. This circuit is designed in 0.18 mm CMOS process. The input voltage range is from 2 V to 3.6 V with the output voltage from 1.8 V to 3.4 V. The efficiency can maintain more than 85% when the load from 50 Ω ~ 1500 Ω for 3.6 V input voltage. The maximum efficiency is 92.4 % at output power to be 38.6 mW for 3.6 V input voltage.Keywords: wireless power transfer, active diode, delay compensation, time to voltage converter, PCE
Procedia PDF Downloads 2581637 Integral Image-Based Differential Filters
Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama
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We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.Keywords: integral images, differential images, differential filters, image fusion
Procedia PDF Downloads 4831636 On the Relation between λ-Symmetries and μ-Symmetries of Partial Differential Equations
Authors: Teoman Ozer, Ozlem Orhan
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This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.Keywords: λ-symmetry, μ-symmetry, classification, invariant solution
Procedia PDF Downloads 2921635 High Efficiency Double-Band Printed Rectenna Model for Energy Harvesting
Authors: Rakelane A. Mendes, Sandro T. M. Goncalves, Raphaella L. R. Silva
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The concepts of energy harvesting and wireless energy transfer have been widely discussed in recent times. There are some ways to create autonomous systems for collecting ambient energy, such as solar, vibratory, thermal, electromagnetic, radiofrequency (RF), among others. In the case of the RF it is possible to collect up to 100 μW / cm². To collect and/or transfer energy in RF systems, a device called rectenna is used, which is defined by the junction of an antenna and a rectifier circuit. The rectenna presented in this work is resonant at the frequencies of 1.8 GHz and 2.45 GHz. Frequencies at 1.8 GHz band are e part of the GSM / LTE band. The GSM (Global System for Mobile Communication) is a frequency band of mobile telephony, it is also called second generation mobile networks (2G), it came to standardize mobile telephony in the world and was originally developed for voice traffic. LTE (Long Term Evolution) or fourth generation (4G) has emerged to meet the demand for wireless access to services such as Internet access, online games, VoIP and video conferencing. The 2.45 GHz frequency is part of the ISM (Instrumentation, Scientific and Medical) frequency band, this band is internationally reserved for industrial, scientific and medical development with no need for licensing, and its only restrictions are related to maximum power transfer and bandwidth, which must be kept within certain limits (in Brazil the bandwidth is 2.4 - 2.4835 GHz). The rectenna presented in this work was designed to present efficiency above 50% for an input power of -15 dBm. It is known that for wireless energy capture systems the signal power is very low and varies greatly, for this reason this ultra-low input power was chosen. The Rectenna was built using the low cost FR4 (Flame Resistant) substrate, the antenna selected is a microfita antenna, consisting of a Meandered dipole, and this one was optimized using the software CST Studio. This antenna has high efficiency, high gain and high directivity. Gain is the quality of an antenna in capturing more or less efficiently the signals transmitted by another antenna and/or station. Directivity is the quality that an antenna has to better capture energy in a certain direction. The rectifier circuit used has series topology and was optimized using Keysight's ADS software. The rectifier circuit is the most complex part of the rectenna, since it includes the diode, which is a non-linear component. The chosen diode is the Schottky diode SMS 7630, this presents low barrier voltage (between 135-240 mV) and a wider band compared to other types of diodes, and these attributes make it perfect for this type of application. In the rectifier circuit are also used inductor and capacitor, these are part of the input and output filters of the rectifier circuit. The inductor has the function of decreasing the dispersion effect on the efficiency of the rectifier circuit. The capacitor has the function of eliminating the AC component of the rectifier circuit and making the signal undulating.Keywords: dipole antenna, double-band, high efficiency, rectenna
Procedia PDF Downloads 1001634 Reduced Differential Transform Methods for Solving the Fractional Diffusion Equations
Authors: Yildiray Keskin, Omer Acan, Murat Akkus
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In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial
Procedia PDF Downloads 5011633 Nonhomogeneous Linear Second Order Differential Equations and Resonance through Geogebra Program
Authors: F. Maass, P. Martin, J. Olivares
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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.Keywords: education, geogebra, ordinary differential equations, resonance
Procedia PDF Downloads 2231632 Weak Solutions Of Stochastic Fractional Differential Equations
Authors: Lev Idels, Arcady Ponosov
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Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others.Keywords: delay equations, operator methods, stochastic noise, weak solutions
Procedia PDF Downloads 1841631 A Continuous Switching Technique for a Single Phase Bridgeless and Transformer-Less Active Rectifier with High Power Factor and Voltage Stabilization
Authors: Rahul Ganpat Mapari, D. G. Wakde
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In this paper, a proposed approach to improve the power factor of single-phase rectifiers and to regulate the output voltage against the change in grid voltage and load is presented. This converter topology is evaluated on the basis of performance and its salient features like simplicity, low cost and high performance are discussed to analyze its applicability. The proposed control strategy is bridgeless, transformer-less and output current sensor-less and consists of only two Bi-directional IGBTs and two diodes. The voltage regulation is achieved by a simple voltage divider to communicate to a controller to control the duty cycles of PWM. A control technique and operational procedure are also developed, both theoretically and experimentally. The experimental results clearly verify the theoretical analysis from the prototype connected to grid unity.Keywords: Active Rectifier (AC-DC), power factor, single phase, voltage regulation
Procedia PDF Downloads 5581630 Generalization of Tau Approximant and Error Estimate of Integral Form of Tau Methods for Some Class of Ordinary Differential Equations
Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed
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An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.Keywords: approximant, error estimate, tau method, overdetermination
Procedia PDF Downloads 5821629 Closed Form Exact Solution for Second Order Linear Differential Equations
Authors: Saeed Otarod
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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra exampleKeywords: explicit, linear, differential, closed form
Procedia PDF Downloads 231628 An Equivalence between a Harmonic Form and a Closed Co-Closed Differential Form in L^Q and Non-L^Q Spaces
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An equivalent relation between a harmonic form and a closed co-closed form is established on a complete non-compact manifold. This equivalence has been generalized for a differential k-form ω from Lq spaces to non-Lq spaces when q=2 in the context of p-balanced growth where p=2. Especially for a simple differential k-form on a complete non-compact manifold, the equivalent relation has been verified with the extended scope of q for from finite q-energy in Lq spaces to infinite q-energy in non-Lq spaces when with 2-balanced growth. Generalized Hadamard Theorem, Cauchy-Schwarz Inequality, and Calculus skills including Integration by Parts as well as Convergent Series have been applied as estimation techniques to evaluate growth rates for a differential form. In particular, energy growth rates as indicated by an appropriate power range in a selected test function lead to a balance between a harmonic differential form and a closed co-closed differential form. Research ideas and computational methods in this paper could provide an innovative way in the study of broadening Lq spaces to non-Lq spaces with a wide variety of infinite energy growth for a differential form.Keywords: closed forms, co-closed forms, harmonic forms, L^q spaces, p-balanced growth, simple differential k-forms
Procedia PDF Downloads 4321627 Strict Stability of Fuzzy Differential Equations by Lyapunov Functions
Authors: Mustafa Bayram Gücen, Coşkun Yakar
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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability
Procedia PDF Downloads 2261626 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, two delays
Procedia PDF Downloads 1851625 Existence of positive periodic solutions for certain delay differential equations
Authors: Farid Nouioua, Abdelouaheb Ardjouni
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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem
Procedia PDF Downloads 4131624 Periodicity of Solutions of a Nonlinear Impulsive Differential Equation with Piecewise Constant Arguments
Authors: Mehtap Lafcı
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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments
Procedia PDF Downloads 4931623 Numerical Treatment of Block Method for the Solution of Ordinary Differential Equations
Authors: A. M. Sagir
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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial 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. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.Keywords: block method, first order ordinary differential equations, hybrid, self-starting
Procedia PDF Downloads 4631622 Sufficient Conditions for Exponential Stability of Stochastic Differential Equations with Non Trivial Solutions
Authors: Fakhreddin Abedi, Wah June Leong
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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula
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