A Haar wavelets method of solving differential equations characterizing the dynamics of a current collection system for an electric locomotive

2015 ◽  
Vol 265 ◽  
pp. 928-935 ◽  
Author(s):  
Chun-Hui Hsiao
Keyword(s):  
Differential Equations ◽  
Haar Wavelets ◽  
Electric Locomotive ◽  
Collection System ◽  
Current Collection ◽  
A Current

The dynamics of a current collection system for an electric locomotive

1971 ◽  
Vol 322 (1551) ◽  
pp. 447-468 ◽  
Keyword(s):  
Contact Force ◽  
Wave Speed ◽  
Operating Conditions ◽  
Electric Locomotive ◽  
Current Collection ◽  
Loss Of Contact ◽  
The Wire ◽  
Linear Differential ◽  
Valid Solution ◽  
A Current

The motion of an overhead trolley wire, suspended at equal intervals by stiff springs, in response to a pantograph moving with constant speed is analysed. The pantograph is modelled by two discrete masses connected by springs and dampers. Away from the supports the inertia and elasticity of the pantograph can be neglected and a simple solution for the wire and pantograph displacement is obtained. Near a support this solution is not valid as it predicts discontinuities in the vertical pantograph velocity. A different first approximation is then required in which the support elasticity and the pantograph inertia and elasticity must be included. This problem is reduced to that of solving a system of four linear differential equations containing one term with a stretched argument. The numerical and asymptotic solution of such a system is discussed and results are obtained for the contact force and pantograph displacement near a support in typical operating conditions. This disturbance at the support is propagated with the wire wave speed and reflected at the subsequent support, thus interacting with the pantograph again. This interaction is analysed and a uniformly valid solution obtained for the contact force over a complete span. Some conclusions are made about possible operating conditions in which loss of contact between the pantograph and the wire may occur.

scholarly journals Green–Haar wavelets method for generalized fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mujeeb ur Rehman ◽  
Dumitru Baleanu ◽  
Jehad Alzabut ◽  
Muhammad Ismail ◽  
Umer Saeed
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Haar Wavelet ◽  
Haar Wavelets ◽  
Computational Time ◽  
Operational Matrices ◽  
Numerical Techniques ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems ◽  
Better Than

Abstract The objective of this paper is to present two numerical techniques for solving generalized fractional differential equations. We develop Haar wavelets operational matrices to approximate the solution of generalized Caputo–Katugampola fractional differential equations. Moreover, we introduce Green–Haar approach for a family of generalized fractional boundary value problems and compare the method with the classical Haar wavelets technique. In the context of error analysis, an upper bound for error is established to show the convergence of the method. Results of numerical experiments have been documented in a tabular and graphical format to elaborate the accuracy and efficiency of addressed methods. Further, we conclude that accuracy-wise Green–Haar approach is better than the conventional Haar wavelets approach as it takes less computational time compared to the Haar wavelet method.

Reconstruction of the parameter in parabolic partial differential equations using Haar wavelet method

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Gopal Priyadarshi ◽  
B.V. Rathish Kumar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Computational Cost ◽  
Haar Wavelet ◽  
Haar Wavelets ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Wavelet Method ◽  
Content Type ◽  
Haar Wavelet Method

Purpose In the past few years, Haar wavelet-based numerical methods have been applied successfully to solve linear and nonlinear partial differential equations. This study aims to propose a wavelet collocation method based on Haar wavelets to identify a parameter in parabolic partial differential equations (PDEs). As Haar wavelet is defined in a very simple way, implementation of the Haar wavelet method becomes easier than the other numerical methods such as finite element method and spectral method. The computational time taken by this method is very less because Haar matrices and Haar integral matrices are stored once and used for each iteration. In the case of Haar wavelet method, Dirichlet boundary conditions are incorporated automatically. Apart from this property, Haar wavelets are compactly supported orthonormal functions. These properties lead to a huge reduction in the computational cost of the method. Design/methodology/approach The aim of this paper is to reconstruct the source control parameter arises in quasilinear parabolic partial differential equation using Haar wavelet-based numerical method. Haar wavelets possess various properties, for example, compact support, orthonormality and closed form expression. The main difficulty with the Haar wavelet is its discontinuity. Therefore, this paper cannot directly use the Haar wavelet to solve partial differential equations. To handle this difficulty, this paper represents the highest-order derivative in terms of Haar wavelet series and using successive integration this study obtains the required term appearing in the problem. Taylor series expansion is used to obtain the second-order partial derivatives at collocation points. Findings An efficient and accurate numerical method based on Haar wavelet has been proposed for parameter identification in quasilinear parabolic partial differential equations. Numerical results are obtained from the proposed method and compared with the existing results obtained from various finite difference methods including Saulyev method. It is shown that the proposed method is superior than the conventional finite difference methods including Saulyev method in terms of accuracy and CPU time. Convergence analysis is presented to show the accuracy of the proposed method. An efficient algorithm is proposed to find the wavelet coefficients at target time. Originality/value The outcome of the paper would have a valuable role in the scientific community for several reasons. In the current scenario, the parabolic inverse problem has emerged as very important problem because of its application in many diverse fields such as tomography, chemical diffusion, thermoelectricity and control theory. In this paper, higher-order derivative is represented in terms of Haar wavelet series. In other words, we represent the solution in multiscale framework. This would enable us to understand the solution at various resolution levels. In the case of Haar wavelet, this paper can achieve a very good accuracy at very less resolution levels, which ultimately leads to huge reduction in the computational cost.

scholarly journals Validation of an Enclosed Blood Collection System in a Pediatric Laboratory

2018 ◽  
Vol 3 (1) ◽  
pp. 65-78
Author(s):  
Elizabeth P Weinzierl ◽  
Cindy Brawley ◽  
James L Adams ◽  
Beverly B Rogers
Keyword(s):  
Clinical Laboratory ◽  
Blood Collection ◽  
Collection System ◽  
Current Collection ◽  
Tube Type ◽  
Clinically Significant ◽  
Almost All ◽  
Automated Instruments ◽  
Adult Volunteers ◽  
Transfer Device

Abstract Background Preanalytical, analytical, and postanalytical issues are often magnified in pediatric laboratories, and traditional vacuum-based blood tubes can contribute to some of these issues. Because of this, we investigated adopting an enclosed blood collection system that can perform vacuum or gentle aspiration blood collection, eliminating syringes, transfer device, and transfer steps, as well as potentially minimizing preanalytical error in the pediatric laboratory. We embarked on a validation of this tube system, in comparison with our current collection tubes, across most in-house tests at a large pediatric hospital. Methods Twenty adult volunteers were recruited. Blood was drawn into lithium heparin, serum, EDTA, and citrate tubes of each commercial tube type for comparison. For some tests, remnant blood from pediatric syringe draws was used when available. Samples were then processed and analyzed across all general areas of the clinical laboratory, and correlations of the results from the 2 tube systems were performed. Results Across 95 tests in the core laboratory and blood bank, almost all demonstrated clinically acceptable comparisons, with most R values >0.90. Only 3 of 95 tests demonstrated clinically significant differences between the tube systems. Conclusions Our validation of the enclosed blood collection system demonstrated acceptable results when compared with our current collection tubes. Additionally, with some minor modifications, our automated instruments could utilize ultralow-volume tubes from the enclosed blood collection system for direct tube sampling, which is impossible using our current small-volume tubes with our main chemistry analyzer.

Numerical Solution for a System of Fractional Differential Equations with Applications in Fluid Dynamics and Chemical Engineering

2017 ◽  
Vol 15 (5) ◽  
Author(s):  
Bijil Prakash ◽  
Amit Setia ◽  
Shourya Bose
Keyword(s):  
Fluid Dynamics ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Numerical Solution ◽  
Fractional Differential Equations ◽  
Crucial Role ◽  
Chemical Engineering ◽  
Haar Wavelets ◽  
Fractional Differential

Abstract In this paper, a Haar wavelets based numerical method to solve a system of linear or nonlinear fractional differential equations has been proposed. Numerous nontrivial test examples along with practical problems from fluid dynamics and chemical engineering have been considered to illustrate applicability of the proposed method. We have derived a theoretical error bound which plays a crucial role whenever the exact solution of the system is not known and also it guarantees the convergence of approximate solution to exact solution.

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