Differential Equations Research Papers - Academia.edu (original) (raw)
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As reported by the World Health Organization, a novel coronavirus (2019-nCoV) was identified as the causative virus of Wuhan pneumonia of unknown etiology by Chinese authorities on 7 January, 2020. The virus was named as severe acute... more
As reported by the World Health Organization, a novel coronavirus (2019-nCoV) was identified as the causative virus of Wuhan pneumonia of unknown etiology by Chinese authorities on 7 January, 2020. The virus was named as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) by International Committee on Taxonomy of Viruses on 11 February, 2020. Keeping in mind the outbreak and rapid spread,this is a mathematical model for calculating the transmissibility of a virus and also identifying preventive measures considering the parameters involved.
A two dimensional model of Series RLC circuit is considered for discussion. The system possess only the trivial equilibrium point and local stability conditions are obtained. The phase portraits are obtained for suitable parameter values.... more
A two dimensional model of Series RLC circuit is considered for discussion. The system possess only the trivial equilibrium point and local stability conditions are obtained. The phase portraits are obtained for suitable parameter values. Oscillations and damping effects are illustrated with numerical examples.
Advection equations appear often in large-scale mathematical models arising in many fields of science and engineering. The Crank-Nicolson scheme can successfully be used in the numerical treatment of such equations. The accuracy of the... more
Advection equations appear often in large-scale mathematical models arising in many fields of science and engineering. The Crank-Nicolson scheme can successfully be used in the numerical treatment of such equations. The accuracy of the numerical solution can sometimes be increased substantially by applying the Richardson Extrapolation. Two theorems related to the accuracy of the calculations will be formulated and proved in this paper. The usefulness of the combination consisting of the Crank-Nicolson scheme and the Richardson Extrapolation will be illustrated by numerical examples.
The power control of wireless networks is formulated using a stochastic optimal control framework, in which the evolution of the channel is described by stochastic differential equations. Under this scenario, average and probabilistic... more
The power control of wireless networks is formulated using a stochastic optimal control framework, in which the evolution of the channel is described by stochastic differential equations. Under this scenario, average and probabilistic Quality of Service (QoS) measures are introduced to evaluate the performance of any control strategy, while a solution of the stochastic optimal power control is obtained through
The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of... more
The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of the proof to partial differential ...
The objective of this work is to make the numerical analysis, through the finite element method with Lagrange’s triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control... more
The objective of this work is to make the numerical analysis, through the finite element method with Lagrange’s triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control variable is the internal energyg. The existence and uniqueness of this continuous optimal control problem and its associated state system were proved previously. In this paper, we discretize the elliptic variational inequality which defines the state system and the corresponding cost functional, and we prove that there exist a discrete optimal control and its associated discrete state system for each positiveh(the parameter of the finite element method approximation). Finally, we show that the discrete optimal control and its associated state system converge to the continuous optimal control and its associated state system when the parameterhgoes to zero.
In this study new iterative method is used for the solution of system of linear differential equations. The solution is obtained in series form and then obtained the exact solution. This shows the efficiency of the new iterative method.... more
In this study new iterative method is used for the solution of system of linear differential equations. The solution is obtained in series form and then obtained the exact solution. This shows the efficiency of the new iterative method. Because using new iterative method we can find its solution easily and more accurately.
An investigation is carried out into the control techniques implemented on a tandem linear direct current machine. The purpose is to control the both motions of the conducting bar such that it moves extremely quickly at the reference... more
An investigation is carried out into the control techniques implemented on a tandem linear direct current machine. The purpose is to control the both motions of the conducting bar such that it moves extremely quickly at the reference velocity of 3.7m/s from the beginning of the rail track to the end of the rail track while bringing itself to a halt at a specific displacement. Standard state variable feedback with pole placement was implemented for controller design to obtain the desired performance specifications and compared with basic linear quadratic control. Simulations conducted revealed that the system dynamics that were set were successfully achieved however there is room for improvement and suggestions for future work is provided. The report concludes that standard pole placement feedback produced better results than linear quadratic control due to the nature of the system.
PROCEDURE Part 1: a) Construct the Series-Parallel Network. Insert the measured value of each resistor. R1 Meas. = 2.15KΩ R1 Calc. = 2.2KΩ R2 Meas. = 0.99 KΩ R2 Calc. = 1KΩ R3 Meas. = 3.3 KΩ R3 Calc. = 3.3KΩ b) Calculate the total... more
PROCEDURE Part 1: a) Construct the Series-Parallel Network. Insert the measured value of each resistor. R1 Meas. = 2.15KΩ R1 Calc. = 2.2KΩ R2 Meas. = 0.99 KΩ R2 Calc. = 1KΩ R3 Meas. = 3.3 KΩ R3 Calc. = 3.3KΩ b) Calculate the total resistance Rt using the measured resistance values and record it. Rt = R1 + (R2//R3) Rt = 2.2KΩ + ((1í µí°¾Ω * 3.3KΩ) (1í µí°¾Ω+3.3í µí°¾Ω)) Rt Calc. = 2.97KΩ Rt Meas. = 2.91KΩ c) Use the ohmmeter section of your multimeter to measure RT and record it. d) Determine the magnitude of the percent difference between the calculated and the measured values of parts 1(b) and 1(c) using the following equation and recorded. % í µí°·í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí±í µí± = | í µí° ¶í µí±í µí±í µí±í µí±¢í µí±í µí±í µí±¡í µí±í µí± − í µí±í µí±í µí±í µí± í µí±¢í µí±í µí±í µí± í µí° ¶í µí±í µí±í µí±í µí±¢í µí±í µí±í µí±¡í µí±í µí± | * 100%
This paper reports the effects of pre- and post-compensation using CRZ modulation format in long-haul WDM optical transmission link using wavelengths in three bandwidths viz. 1537.4; 1550; 1562.6 nm at per channel bit rates of 10 Gbit/s.... more
This paper reports the effects of pre- and post-compensation using CRZ modulation format in long-haul WDM optical transmission link using wavelengths in three bandwidths viz. 1537.4; 1550; 1562.6 nm at per channel bit rates of 10 Gbit/s. It has been investigated here that optimization of dispersion map results in improved management of nonlinear effects in long-haul light wave systems operating in the quasi-linear regime. In addition, pre- and post-dispersion compensation was applied at the transmitter and receiver depending on the signal wavelength, which resulted in improvement of performance metrics viz. Q2 (dB), BER and OSNR over longer transmission distances. It is reported here that optimum values of Q2 dB of 17.1 dB, BER of 8.4933e−015 and OSNR of 30.1 dB are obtained at 1550 nm at a transmission distance of 7360 km with pre- and post-compensation using CRZ modulation format.
A method for computing Mackey-Glass equation of the form () (), () y t f y t y t is examined in this paper. For a given lag , uniformly generated and fixed beta is observed for estimating the y (density time-units in the... more
A method for computing Mackey-Glass equation of the form () (), () y t f y t y t is examined in this paper. For a given lag , uniformly generated and fixed beta is observed for estimating the y (density time-units in the past). The technique was applied to blood destruction and production in human body.