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 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 AN APPROXIMATE BOUNDARY INTEGRAL METHOD FOR ACOUSTIC SCATTERING IN SHALLOW OCEANS

1993 ◽  
Vol 01 (01) ◽  
pp. 61-75 ◽  
Author(s):  
YONGZHI XU ◽  
YI YAN
Keyword(s):  
Integral Equation ◽  
Wave Scattering ◽  
Integral Method ◽  
Acoustic Scattering ◽  
Quadrature Rule ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Acoustic Wave Scattering ◽  
Sea Bottom ◽  
Time Harmonic

The problem of a time-harmonic acoustic wave scattering from a cylindrical object in shallow oceans is solved by an approximate boundary integral method. In the method we employ a Green's function of the Helmholtz equation with sound soft sea level and sound hard sea bottom conditions, and reformulate the problem into a boundary integral equation on the surface of the scattering object. The kernel of the integral equation is given by an infinite series, and is approximated by an appropriate truncation. The integral equation is then fully discretized by applying a quadrature rule. The method has an O(N−3) rate of convergence. Various numerical examples are presented.

scholarly journals Mathematical Modelling of Acetaminophen Release in HPC/PAAm Hydrogel: Synthesis and Application

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Abigail M. Díaz-Guerrero ◽  
Claudia A. Castillo-Miranda ◽  
Carlos F. Castro-Guerrero ◽  
Hernán Peraza-Vázquez ◽  
Ana B. Morales-Cepeda ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Phosphate Buffer Solution ◽  
Absolute Error ◽  
Programming Algorithm ◽  
Test Results ◽  
Buffer Solution ◽  
Drug Molecules ◽  
Hydrogel Synthesis ◽  
The Mathematical Model

Hydrogels are commonly used as Drug Delivery Systems (DDS) as patches due to its ability to store drug molecules within their structures. The release can be activated under certain stimuli, such as temperature and pH. In this paper, the mathematical modelling of acetaminophen release in hydroxypropyl cellulose with polyacrylamide (HPC/PAAm) is reported. The HPC/PAAm gel was synthesized in proportions of 25/75 wt% and was characterized by FTIR, DSC, optical microscopy, SEM, and TGA, with and without acetaminophen. The release tests were performed for hypothermic, normal, and febrile human body conditions, at 35, 37, and 39°C, respectively, on two release media: water and phosphate buffer solution. In order to describe the release of acetaminophen in HPC/PAAm gel, a genetic programming algorithm was used to accomplish Multigene Symbolic Regression (MSR). Characterization results showed that the drug was crystallized on the surface of the HPC/PAAm gel. Release test results showed that several simultaneous processes occurred in the acetaminophen diffusion phenomenon. A unique mathematical model was obtained by MSR. This model was able to describe the release of acetaminophen in HPC/PAAm gel with high values of R2 and adjusted R2 and to simulate the drug release at times beyond the end of the experiment. High values of R2 and low values of Coefficient of Variation (CV), Root-Mean-Square Error (RMSE), and Mean Absolute Error (MAE) were obtained from the comparison between the simulated and the experimental data. This allows to conclude that the mathematical model is reliable to represent and simulate the acetaminophen release in HPC/PAAm gel at 35, 37, and 39°C.

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 .

scholarly journals Numerical treatment of the generalized Love integral equation

2020 ◽  
Author(s):  
Luisa Fermo ◽  
Maria Grazia Russo ◽  
Giada Serafini
Keyword(s):  
Integral Equation ◽  
Quadrature Formula ◽  
Numerical Procedure ◽  
Quadrature Rule ◽  
Weighted Spaces ◽  
Stability And Convergence ◽  
Numerical Treatment ◽  
Nyström Method ◽  
Numerical Tests ◽  
The Stability

Abstract In this paper, the generalized Love integral equation has been considered. In order to approximate the solution, a Nyström method based on a mixed quadrature rule has been proposed. Such a rule is a combination of a product and a “dilation” quadrature formula. The stability and convergence of the described numerical procedure have been discussed in suitable weighted spaces and the efficiency of the method is shown by some numerical tests.

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 SOLUTION OF CONTACT PROBLEM FOR AN ARC CRACK USING HYPERSINGULAR INTEGRAL EQUATION

2008 ◽  
Vol 05 (01) ◽  
pp. 119-133 ◽  
Author(s):  
Y. Z. CHEN ◽  
X. Y. LIN ◽  
Z. X. WANG ◽  
N. M. A. NIK LONG
Keyword(s):  
Integral Equation ◽  
Contact Problem ◽  
Quadrature Rule ◽  
Plane Elasticity ◽  
Hypersingular Integral Equation ◽  
Normal Contact Stress ◽  
Normal Contact ◽  
Hypersingular Integral ◽  
Numerical Examples ◽  
Arc Crack

This paper investigates the contact problem for an arc crack, for example, under a remote compression. A hypersingular integral equation (HSIE) for curved cracks in plane elasticity is suggested. It is found that the direct usage of HSIE cannot solve the mentioned contact problem. For the contact problem, one must take necessary modifications for solving the HSIE. The main modified points are as follows. First, one should assume some portion along the crack under contact. The margin or the end of the contacted portion is determined by the vanishing normal contact stress at the margin point. In addition, it is found that a suggested quadrature rule in conjunction with the curve length method provides a very effective way to solve the HSIE. Finally, several numerical examples are given.

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 On mathematical modelling of temporal spatial spread of epidemics

2020 ◽  
Vol 15 ◽  
pp. 6
Author(s):  
Kh.A. Khachatryan ◽  
A.Zh. Narimanyan ◽  
A.Kh. Khachatryan
Keyword(s):  
Integral Equation ◽  
Mathematical Modelling ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Spatial Spread ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Convergence Results ◽  
Integral Differential Equations ◽  
Multidimensional Integral

In the present work a generalized epidemic model containing a system of integral-differential equations is described. Using different transformations the system is reduced to a single nonlinear multidimensional integral equation. For the obtained equation the existence and uniqueness results are proved. Based on theoretical convergence results several application examples are presented with corresponding numerical results.

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