scholarly journals Approximate instantneous current in RLC circuit

2020 ◽  
Vol 9 (2) ◽  
pp. 801-807
Author(s):  
Saumya Ranjan Jena ◽  
Damayanti Nayak
Keyword(s):  
Integral Equation ◽  
Electromotive Force ◽  
Absolute Error ◽  
Definite Integral ◽  
Numerical Result ◽  
Rlc Circuit ◽  
Instantaneous Current

In this study, a mixed rule of degree of precision nine has been developed and implemented in the field of electrical sciences to obtain the instantaneous current in the RLC- circuit for particular value .The linearity has been performed with the Volterra’s  integral equation of second kind with particular kernel . Then the definite integral has been evaluated through the mixed quadrature to obtain the numerical result which is very effective. A polynomial has been used to evaluate Volterra’s integral equation in the place of unknown functions. The accuracy of the proposed method has been tested taking different electromotive force in the circuit and absolute error has been estimated.

scholarly journals Mathematical Modelling of  RLC Circuit  Through Mixed Quadrature Rule

2018 ◽  
Author(s):  
Saumya jena ◽  
Damayanti Nayak
Keyword(s):  
Integral Equation ◽  
Mathematical Modelling ◽  
Electromotive Force ◽  
Quadrature Rule ◽  
Absolute Error ◽  
Definite Integral ◽  
Numerical Result ◽  
Rlc Circuit ◽  
Instantaneous Current

In this study, a mixed rule of degree of precision nine has been developed and implemented in the field of electrical sciences to obtain the instantaneous current in the RLC- circuit for particular value .The linearity has been performed with the Volterra’s integral equation of second kind with particular kernel . Then the definite integral has been evaluated through the mixed quadrature to obtain the numerical result which is very effective. A polynomial has been used to evaluate Volterra’s integral equation in the place of unknown functions. The accuracy of the proposed method has been tested taking different electromotive force in the circuit and absolute error has been estimated.

scholarly journals Numerical and analytic method for solvingproposal New Type for fuzzy nonlinear volterra integral equation

2016 ◽  
Vol 12 (5) ◽  
pp. 6207-6231
Author(s):  
Sameer Qasim Hasan ◽  
Alan Abdulqader Jalal
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Homotopy Analysis Method ◽  
Absolute Error ◽  
Analytic Method ◽  
Analysis Method ◽  
Nonlinear Volterra Integral Equation ◽  
Homotopy Analysis ◽  
New Type ◽  
Fuzzy Solution

In this paper, we proved the existence and uniqueness and convergence of the solution of new type for nonlinear fuzzy volterra integral equation . The homotopy analysis method are proposed to solve the new type fuzzy nonlinear Volterra integral equation . We convert a fuzzy volterra integral equation for new type of kernel for integral equation, to a system of crisp function nonlinear volterra integral equation . We use the homotopy analysis method to find the approximate solution of the system and hence obtain an approximation for fuzzy solution of the nonlinear fuzzy volterra integral equation . Some numerical examples is given and results reveal that homotopy analysis method is very effective and compared with the exact solution and calculate the absolute error between the exact and AHM .Finally using the MAPLE program to solve our problem .

Dynamic Inversion Guidance Law for a Hypersonic Vehicle

2011 ◽  
Vol 383-390 ◽  
pp. 4451-4456
Author(s):  
Qing Qing Qiao ◽  
Wan Chun Chen
Keyword(s):  
Performance Index ◽  
Optimal Trajectory ◽  
Absolute Error ◽  
Hypersonic Vehicle ◽  
Pid Controllers ◽  
Dynamic Inversion ◽  
Numerical Result ◽  
Guidance Law ◽  
Optimal Guidance ◽  
Maximum Range

An adapting dynamic inversion guidance law developed by using integral of time multiply by absolute error (ITAE) performance index for a hypersonic vehicle was studied. As a nominal trajectory, Maximum-Range glide trajectory was obtained by using collocation and successive quadratic programming. Dynamic inversion technique was employed to produce a guidance law which contains two PID controllers. To find optimal guidance parameters, ITAE criteria were used to tune the PID parameters. The numerical result showed that the guidance law was simple and efficient for a hypersonic vehicle flies along the optimal trajectory.

scholarly journals Proof of Goldbach Conjecture

2014 ◽  
Vol 7 ◽  
pp. 1-8
Author(s):  
Ren Yong Xue ◽  
Ren Yi
Keyword(s):  
Integral Equation ◽  
Coordinate System ◽  
Integration Method ◽  
Prime Numbers ◽  
Definite Integral ◽  
Rectangular Coordinate System ◽  
Coordinate Axis ◽  
The Creation ◽  
Infinite Sets

This paper through the creation of "double rectangular coordinate system", within the I quadrants, each coordinate axis coordinates all constitute the infinite sets. Coordinates with infinite sets one toone correspondence between the elements within and equal relationship. With any of the sum of two odd prime Numbers (a + b) to form a square area, length for a quarter of a square area A1 "square" diagonal integration method, a quarter of a square area A1 equation is derived with the definite integral equation; A1 area value of the argument as infinite generalized integral value, and deduce the equations, the Goldbach conjecture.

scholarly journals Advantages of the Discrete Stochastic Arithmetic to Validate the Results of the Taylor Expansion Method to Solve the Generalized Abel’s Integral Equation

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1370
Author(s):  
Eisa Zarei ◽  
Samad Noeiaghdam
Keyword(s):  
Integral Equation ◽  
Taylor Expansion ◽  
Expansion Method ◽  
Absolute Error ◽  
Optimal Error ◽  
Cestac Method ◽  
Stochastic Arithmetic ◽  
Cadna Library ◽  
Numerical Instabilities ◽  
Termination Criterion

The aim of this paper is to apply the Taylor expansion method to solve the first and second kinds Volterra integral equations with Abel kernel. This study focuses on two main arithmetics: the FPA and the DSA. In order to apply the DSA, we use the CESTAC method and the CADNA library. Using this method, we can find the optimal step of the method, the optimal approximation, the optimal error, and some of numerical instabilities. They are the main novelties of the DSA in comparison with the FPA. The error analysis of the method is proved. Furthermore, the main theorem of the CESTAC method is presented. Using this theorem we can apply a new termination criterion instead of the traditional absolute error. Several examples are approximated based on the FPA and the DSA. The numerical results show the applications and advantages of the DSA than the FPA.

Sex Differences in Time Production Revisited

2012 ◽  
Vol 33 (1) ◽  
pp. 35-42 ◽  
Author(s):  
Joseph Glicksohn ◽  
Yamit Hadad
Keyword(s):  
Sex Differences ◽  
Individual Differences ◽  
Sex Difference ◽  
Absolute Error ◽  
Internal Clock ◽  
Target Duration ◽  
Log P ◽  
Men And Women ◽  
Time Production ◽  
T Score

Individual differences in time production should indicate differences in the rate of functioning of an internal clock, assuming the existence of such a clock. And sex differences in time production should reflect a difference in the rate of functioning of that clock between men and women. One way of approaching the data is to compute individual regressions of produced duration (P) on target duration (T), after log transformation, and to derive estimates for the intercept and the slope. One could investigate a sex difference by comparing these estimates for men and women; one could also contrast them by looking at mean log(P). Using such indices, we found a sex difference in time production, female participants having a relatively faster internal clock, making shorter time productions, and having a smaller exponent. The question is whether a sex difference in time production would be found using other methods for analyzing the data: (1) the P/T ratio; (2) an absolute discrepancy (|P-T|) score; and (3) an absolute error (|P-T|/T) score. For the P/T ratio, female participants have a lower mean ratio in comparison to the male participants. In contrast, the |P-T| and |P-T|/T indices seem to be seriously compromised by wide individual differences.

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