Search results for: gradient method.
8027 Two-Dimensional Solitary Wave Solution to the Quadratic Nonlinear Schrdinger Equation
Authors: Sarun Phibanchon
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The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.
Keywords: soliton, iterative method, spectral method, plasma
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18678026 The Reliability of the Improved e-N Method for Transition Prediction as Checked by PSE Method
Authors: Caihong Su
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Transition prediction of boundary layers has always been an important problem in fluid mechanics both theoretically and practically, yet notwithstanding the great effort made by many investigators, there is no satisfactory answer to this problem. The most popular method available is so-called e-N method which is heavily dependent on experiments and experience. The author has proposed improvements to the e-N method, so to reduce its dependence on experiments and experience to a certain extent. One of the key assumptions is that transition would occur whenever the velocity amplitude of disturbance reaches 1-2% of the free stream velocity. However, the reliability of this assumption needs to be verified. In this paper, transition prediction on a flat plate is investigated by using both the improved e-N method and the parabolized stability equations (PSE) methods. The results show that the transition locations predicted by both methods agree reasonably well with each other, under the above assumption. For the supersonic case, the critical velocity amplitude in the improved e-N method should be taken as 0.013, whereas in the subsonic case, it should be 0.018, both are within the range 1-2%.Keywords: Boundary layer, e-N method, PSE, Transition
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15108025 Variational Iteration Method for the Solution of Boundary Value Problems
Authors: Olayiwola M.O., Gbolagade A .W., Akinpelu F. O.
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In this work, we present a reliable framework to solve boundary value problems with particular significance in solid mechanics. These problems are used as mathematical models in deformation of beams. The algorithm rests mainly on a relatively new technique, the Variational Iteration Method. Some examples are given to confirm the efficiency and the accuracy of the method.
Keywords: Variational iteration method, boundary value problems, convergence, restricted variation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21108024 Deep Learning for Renewable Power Forecasting: An Approach Using LSTM Neural Networks
Authors: Fazıl Gökgöz, Fahrettin Filiz
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Load forecasting has become crucial in recent years and become popular in forecasting area. Many different power forecasting models have been tried out for this purpose. Electricity load forecasting is necessary for energy policies, healthy and reliable grid systems. Effective power forecasting of renewable energy load leads the decision makers to minimize the costs of electric utilities and power plants. Forecasting tools are required that can be used to predict how much renewable energy can be utilized. The purpose of this study is to explore the effectiveness of LSTM-based neural networks for estimating renewable energy loads. In this study, we present models for predicting renewable energy loads based on deep neural networks, especially the Long Term Memory (LSTM) algorithms. Deep learning allows multiple layers of models to learn representation of data. LSTM algorithms are able to store information for long periods of time. Deep learning models have recently been used to forecast the renewable energy sources such as predicting wind and solar energy power. Historical load and weather information represent the most important variables for the inputs within the power forecasting models. The dataset contained power consumption measurements are gathered between January 2016 and December 2017 with one-hour resolution. Models use publicly available data from the Turkish Renewable Energy Resources Support Mechanism. Forecasting studies have been carried out with these data via deep neural networks approach including LSTM technique for Turkish electricity markets. 432 different models are created by changing layers cell count and dropout. The adaptive moment estimation (ADAM) algorithm is used for training as a gradient-based optimizer instead of SGD (stochastic gradient). ADAM performed better than SGD in terms of faster convergence and lower error rates. Models performance is compared according to MAE (Mean Absolute Error) and MSE (Mean Squared Error). Best five MAE results out of 432 tested models are 0.66, 0.74, 0.85 and 1.09. The forecasting performance of the proposed LSTM models gives successful results compared to literature searches.Keywords: Deep learning, long-short-term memory, energy, renewable energy load forecasting.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16038023 Haar Wavelet Method for Solving Fitz Hugh-Nagumo Equation
Authors: G.Hariharan, K.Kannan
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In this paper, we develop an accurate and efficient Haar wavelet method for well-known FitzHugh-Nagumo equation. The proposed scheme can be used to a wide class of nonlinear reaction-diffusion equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.
Keywords: FitzHugh-Nagumo equation, Haar wavelet method, adomain decomposition method, computationally attractive.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27878022 Control of Pressure Gradient in the Contraction of a Wind Tunnel
Authors: Dehghan Manshadi M., Mirzaei M., Soltani M. R., Ghorbanian K.
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Subsonic wind tunnel experiments were conducted to study the effect of tripped boundary layer on the pressure distribution in the contraction region of the tunnel. Measurements were performed by installing trip strip at two different positions in the concave portion of the contraction. The results show that installation of the trip strips, have significant effects on both turbulence and pressure distribution. The reduction in the free stream turbulence and reduction of the wall static pressure distribution deferred signified with the location of the trip strip.Keywords: Contraction, pressure distribution, trip strip, turbulence intensity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 30438021 Octonionic Reformulation of Vector Analysis
Authors: Bhupendra C. S. Chauhan, P. S. Bisht, O. P. S. Negi
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According to celebrated Hurwitz theorem, there exists four division algebras consisting of R (real numbers), C (complex numbers), H (quaternions) and O (octonions). Keeping in view the utility of octonion variable we have tried to extend the three dimensional vector analysis to seven dimensional one. Starting with the scalar and vector product in seven dimensions, we have redefined the gradient, divergence and curl in seven dimension. It is shown that the identity n(n - 1)(n - 3)(n - 7) = 0 is satisfied only for 0, 1, 3 and 7 dimensional vectors. We have tried to write all the vector inequalities and formulas in terms of seven dimensions and it is shown that same formulas loose their meaning in seven dimensions due to non-associativity of octonions. The vector formulas are retained only if we put certain restrictions on octonions and split octonions.Keywords: Octonions, Vector Space and seven dimensions
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12058020 A Method for Measurement and Evaluation of Drape of Textiles
Authors: L. Fridrichova, R. Knížek, V. Bajzík
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Drape is one of the important visual characteristics of the fabric. This paper is introducing an innovative method of measurement and evaluation of the drape shape of the fabric. The measuring principle is based on the possibility of multiple vertical strain of the fabric. This method more accurately simulates the real behavior of the fabric in the process of draping. The method is fully automated, so the sample can be measured by using any number of cycles in any time horizon. Using the present method of measurement, we are able to describe the viscoelastic behavior of the fabric.
Keywords: Drape, drape shape, automated drape meter.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8838019 Seat Assignment Model for Student Admissions Process at Saudi Higher Education Institutions
Authors: Mohammed Salem Alzahrani
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In this paper, student admission process is studied to optimize the assignment of vacant seats with three main objectives. Utilizing all vacant seats, satisfying all programs of study admission requirements and maintaining fairness among all candidates are the three main objectives of the optimization model. Seat Assignment Method (SAM) is used to build the model and solve the optimization problem with help of Northwest Coroner Method and Least Cost Method. A closed formula is derived for applying the priority of assigning seat to candidate based on SAM.
Keywords: Admission Process Model, Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19798018 A Dual Method for Solving General Convex Quadratic Programs
Authors: Belkacem Brahmi, Mohand Ouamer Bibi
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In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated problems.
Keywords: Convex quadratic programming, dual support methods, active set methods.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18998017 Zero-Dissipative Explicit Runge-Kutta Method for Periodic Initial Value Problems
Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok
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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.
Keywords: Dissipation, Oscillatory solutions, Phase-lag, Runge- Kutta methods.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19108016 Selection Initial modes for Belief K-modes Method
Authors: Sarra Ben Hariz, Zied Elouedi, Khaled Mellouli
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The belief K-modes method (BKM) approach is a new clustering technique handling uncertainty in the attribute values of objects in both the cluster construction task and the classification one. Like the standard version of this method, the BKM results depend on the chosen initial modes. So, one selection method of initial modes is developed, in this paper, aiming at improving the performances of the BKM approach. Experiments with several sets of real data show that by considered the developed selection initial modes method, the clustering algorithm produces more accurate results.Keywords: Clustering, Uncertainty, Belief function theory, Belief K-modes Method, Initial modes selection.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18218015 Variational Iteration Method for Solving Systems of Linear Delay Differential Equations
Authors: Sara Barati, Karim Ivaz
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In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.
Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24878014 Comparison of Finite-Element and IEC Methods for Cable Thermal Analysis under Various Operating Environments
Authors: M. S. Baazzim, M. S. Al-Saud, M. A. El-Kady
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In this paper, steady-state ampacity (current carrying capacity) evaluation of underground power cable system by using analytical and numerical methods for different conditions (depth of cable, spacing between phases, soil thermal resistivity, ambient temperature, wind speed), for two system voltage level were used 132 and 380 kV. The analytical method or traditional method that was used is based on the thermal analysis method developed by Neher-McGrath and further enhanced by International Electrotechnical Commission (IEC) and published in standard IEC 60287. The numerical method that was used is finite element method and it was recourse commercial software based on finite element method.
Keywords: Cable ampacity, Finite element method, underground cable, thermal rating.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 58678013 Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Clenshaw Method
Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei
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As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14268012 Application of Homotopy Perturbation Method to Solve Steady Flow of Walter B Fluid A Vertical Channel In Porous Media
Authors: A.Memari
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In this article, a simulation method called the Homotopy Perturbation Method (HPM) is employed in the steady flow of a Walter's B' fluid in a vertical channel with porous wall. We employed Homotopy Perturbation Method to derive solution of a nonlinear form of equation obtained from exerting similarity transforming to the ordinary differential equation gained from continuity and momentum equations of this kind of flow. The results obtained from the Homotopy Perturbation Method are then compared with those from the Runge–Kutta method in order to verify the accuracy of the proposed method. The results show that the Homotopy Perturbation Method can achieve good results in predicting the solution of such problems. Ultimately we use this solution to obtain the other terms of velocities and physical discussion about it.
Keywords: Steady flow; Walter's B' Fluid;, vertical channel;porous media, Homotopy Perturbation Method (HPM), Numerical Solution (NS).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19848011 Sparsity-Aware Affine Projection Algorithm for System Identification
Authors: Young-Seok Choi
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This work presents a new type of the affine projection (AP) algorithms which incorporate the sparsity condition of a system. To exploit the sparsity of the system, a weighted l1-norm regularization is imposed on the cost function of the AP algorithm. Minimizing the cost function with a subgradient calculus and choosing two distinct weighting for l1-norm, two stochastic gradient based sparsity regularized AP (SR-AP) algorithms are developed. Experimental results exhibit that the SR-AP algorithms outperform the typical AP counterparts for identifying sparse systems.Keywords: System identification, adaptive filter, affine projection, sparsity, sparse system.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15588010 Texture Feature Extraction of Infrared River Ice Images using Second-Order Spatial Statistics
Authors: Bharathi P. T, P. Subashini
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Ice cover County has a significant impact on rivers as it affects with the ice melting capacity which results in flooding, restrict navigation, modify the ecosystem and microclimate. River ices are made up of different ice types with varying ice thickness, so surveillance of river ice plays an important role. River ice types are captured using infrared imaging camera which captures the images even during the night times. In this paper the river ice infrared texture images are analysed using first-order statistical methods and secondorder statistical methods. The second order statistical methods considered are spatial gray level dependence method, gray level run length method and gray level difference method. The performance of the feature extraction methods are evaluated by using Probabilistic Neural Network classifier and it is found that the first-order statistical method and second-order statistical method yields low accuracy. So the features extracted from the first-order statistical method and second-order statistical method are combined and it is observed that the result of these combined features (First order statistical method + gray level run length method) provides higher accuracy when compared with the features from the first-order statistical method and second-order statistical method alone.
Keywords: Gray Level Difference Method, Gray Level Run Length Method, Kurtosis, Probabilistic Neural Network, Skewness, Spatial Gray Level Dependence Method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 29158009 A Method for Improving the Embedded Runge Kutta Fehlberg 4(5)
Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim
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In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.
Keywords: Embedded Runge-Kutta-Fehlberg method, Initial value problem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27568008 Stating Best Commercialization Method: An Unanswered Question from Scholars and Practitioners
Authors: Saheed A. Gbadegeshin
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Commercialization method is a means to make inventions available at the market for final consumption. It is described as an important tool for keeping business enterprises sustainable and improving national economic growth. Thus, there are several scholarly publications on it, either presenting or testing different methods for commercialization. However, young entrepreneurs, technologists and scientists would like to know the best method to commercialize their innovations. Then, this question arises: What is the best commercialization method? To answer the question, a systematic literature review was conducted, and practitioners were interviewed. The literary results revealed that there are many methods but new methods are needed to improve commercialization especially during these times of economic crisis and political uncertainty. Similarly, the empirical results showed there are several methods, but the best method is the one that reduces costs, reduces the risks associated with uncertainty, and improves customer participation and acceptability. Therefore, it was concluded that new commercialization method is essential for today's high technologies and a method was presented.
Keywords: Commercialization method, high technology, lean start-up methodology, technology, knowledge.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13058007 An Eulerian Numerical Method and its Application to Explosion Problems
Authors: Li Hao, Yan Zhang, Jingan Cui
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The Eulerian numerical method is proposed to analyze the explosion in tunnel. Based on this method, an original software M-MMIC2D is developed by Cµ program language. With this software, the explosion problem in the tunnel with three expansion-chambers is numerically simulated, and the results are found to be in full agreement with the observed experimental data.Keywords: Eulerian method, numerical simulation, shock wave, tunnel
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14608006 Method for Solving Fully Fuzzy Assignment Problems Using Triangular Fuzzy Numbers
Authors: Amit Kumar, Anila Gupta, Amarpreet Kaur
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In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy assignment problems by representing all the parameters as triangular fuzzy numbers. The advantages of the pro-posed method are also discussed. To illustrate the proposed method a fuzzy assignment problem is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy assignment problems occurring in real life situations.
Keywords: Fuzzy assignment problem, Ranking function, Triangular fuzzy numbers.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17098005 High Resolution Methods Based On Rank Revealing Triangular Factorizations
Authors: M. Bouri, S. Bourennane
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In this paper, we propose a novel method for subspace estimation used high resolution method without eigendecomposition where the sample Cross-Spectral Matrix (CSM) is replaced by upper triangular matrix obtained from LU factorization. This novel method decreases the computational complexity. The method relies on a recently published result on Rank-Revealing LU (RRLU) factorization. Simulation results demonstrates that the new algorithm outperform the Householder rank-revealing QR (RRQR) factorization method and the MUSIC in the low Signal to Noise Ratio (SNR) scenarios.
Keywords: Factorization, Localization, Matrix, Signalsubspace.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13638004 A Method for Modeling Flexible Manipulators: Transfer Matrix Method with Finite Segments
Authors: Haijie Li, Xuping Zhang
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This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.Keywords: Flexible manipulator, transfer matrix method, linearization, finite segment method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19688003 Application of Novel Conserving Immersed Boundary Method to Moving Boundary Problem
Authors: S. N. Hosseini, S. M. H. Karimian
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A new conserving approach in the context of Immersed Boundary Method (IBM) is presented to simulate one dimensional, incompressible flow in a moving boundary problem. The method employs control volume scheme to simulate the flow field. The concept of ghost node is used at the boundaries to conserve the mass and momentum equations. The Present method implements the conservation laws in all cells including boundary control volumes. Application of the method is studied in a test case with moving boundary. Comparison between the results of this new method and a sharp interface (Image Point Method) IBM algorithm shows a well distinguished improvement in both pressure and velocity fields of the present method. Fluctuations in pressure field are fully resolved in this proposed method. This approach expands the IBM capability to simulate flow field for variety of problems by implementing conservation laws in a fully Cartesian grid compared to other conserving methods.
Keywords: Immersed Boundary Method, conservation of mass and momentum laws, moving boundary, boundary condition.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19958002 The Comprehensive Study Based on Ultrasonic and X-ray Visual Technology for GIS Equipment Detection
Authors: Wei Zhang, Hong Yu, Xian-ping Zhao, Da-da Wang, Fei Xue
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For lack of the visualization of the ultrasonic detection method of partial discharge (PD), the ultrasonic detection technology combined with the X-ray visual detection method (UXV) is proposed. The method can conduct qualitative analysis accurately and conduct reliable positioning diagnosis to the internal insulation defects of GIS, and while it could make up the blindness of the X-ray visual detection method and improve the detection rate. In this paper, an experimental model of GIS is used as the trial platform, a variety of insulation defects are set inside the GIS cavity. With the proposed method, the ultrasonic method is used to conduct the preliminary detection, and then the X-ray visual detection is used to locate and diagnose precisely. Therefore, the proposed UXV technology is feasible and practical.Keywords: GIS, ultrasonic, visual detection, X-ray
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17278001 Septic B-Spline Collocation Method for Numerical Solution of the Kuramoto-Sivashinsky Equation
Authors: M. Zarebnia, R. Parvaz
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In this paper the Kuramoto-Sivashinsky equation is solved numerically by collocation method. The solution is approximated as a linear combination of septic B-spline functions. Applying the Von-Neumann stability analysis technique, we show that the method is unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The global relative error and L∞ in the solutions show the efficiency of the method computationally.
Keywords: Kuramoto-Sivashinsky equation, Septic B-spline, Collocation method, Finite difference.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20678000 An Optimization of Orbital Transfer for Spacecrafts with Finite-thrust Based on Legendre Pseudospectral Method
Authors: Yanan Yang, Zhigang Wang, Xiang Chen
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This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System-s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transform the optimal control problem into a constrained parameter optimization problem. The developed novel optimization algorithm can be used to solve similar optimization problems of spacecraft finite-thrust orbital transfer. The results of a numerical simulation verified the validity of the proposed optimization method. The simulation results reveal that pseudospectral optimization method is a promising method for real-time trajectory optimization and provides good accuracy and fast convergence.Keywords: Finite-thrust, Orbital transfer, Legendre pseudospectral method
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18117999 A Contractor Iteration Method Using Eigenpairs for Positive Solutions of Nonlinear Elliptic Equation
Authors: Hailong Zhu, Zhaoxiang Li, Kejun Zhuang
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By means of Contractor Iteration Method, we solve and visualize the Lane-Emden(-Fowler) equation Δu + up = 0, in Ω, u = 0, on ∂Ω. It is shown that the present method converges quadratically as Newton’s method and the computation of Contractor Iteration Method is cheaper than the Newton’s method.
Keywords: Positive solutions, newton's method, contractor iteration method, Eigenpairs.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13817998 Sewer Culvert Installation Method to Accommodate Underground Construction in an Urban Area with Narrow Streets (The Development of Shield Switching Type Micro-Tunneling Method and the Introduction of Construction Examples)
Authors: Osamu Igawa, Hiroshi Kouchiwa, Yuji Ito
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In recent years, a reconstruction project for sewer pipelines has been progressing in Japan with the aim of renewing old sewer culverts. However, it is difficult to secure a sufficient base area for shafts in an urban area because many streets are narrow with a complex layout. As a result, construction in such urban areas is generally very demanding. In urban areas, there is a strong requirement for a safe, reliable and economical construction method that does not disturb the public’s daily life and urban activities. With this in mind, we developed a new construction method called the “shield switching type micro-tunneling method,” which integrates the micro-tunneling method and shield method. In this method, pipeline is constructed first for sections that are gently curved or straight using the economical micro-tunneling method, and then the method is switched to the shield method for sections with a sharp curve or a series of curves without establishing an intermediate shaft. This paper provides the information, features and construction examples of this newly developed method.
Keywords: Micro-tunneling method, Secondary lining applied RC segment, Sharp curve, Shield method, Switching type.
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