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Yao-lin Jiang - One of the best experts on this subject based on the ideXlab platform.
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Symplectic waveform Relaxation Methods for Hamiltonian systems
Applied Mathematics and Computation, 2017Co-Authors: Yao-lin Jiang, Bo SongAbstract:In this literature, a new Method called symplectic waveform Relaxation Method is for the first time proposed to solve Hamiltonian systems. This Method is based on waveform Relaxation Method which makes computation cheaper, and makes use of symplectic Method to determine its numerical scheme. Under the guidance of the symplectic Method, the discrete waveform Relaxation Method elegantly preserves the discrete symplectic form. Windowing technique is utilized to accelerate computation. The windowing technique also makes it possible to advance in time, window by window. Convergence results of continuous and discrete symplectic waveform Relaxation Methods are analyzed. Numerical results show that the symplectic waveform Relaxation Method with the windowing technique precisely preserves the Hamiltonian function.
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Waveform Relaxation Method for fractional differential-algebraic equations
Fractional Calculus and Applied Analysis, 2014Co-Authors: Xiao-li Ding, Yao-lin JiangAbstract:The waveform Relaxation Method has been successfully applied into solving fractional ordinary differential equations and fractional functional differential equations [11, 5]. In this paper, the waveform Relaxation Method is further used to solve fractional differential-algebraic equations, which often arise in integrated circuits with new memory materials. We give the iteration scheme of the waveform Relaxation Method and analyze the convergence of the Method under linear and nonlinear conditions for the right-hand of the equations. Numerical examples illustrate the feasibility and efficiency of the Method.
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A note on the H1-convergence of the overlapping Schwarz waveform Relaxation Method for the heat equation
Numerical Algorithms, 2013Co-Authors: Hui Zhang, Yao-lin JiangAbstract:The overlapping Schwarz waveform Relaxation Method is a parallel iterative Method for solving time-dependent PDEs. Convergence of the Method for the linear heat equation has been studied under infinity norm but it was unknown under the energy norm at the continuous level. The question is interesting for applications concerning fluxes or gradients of the solutions. In this work, we show that the energy norm of the errors of iterates is bounded by their infinity norm. Therefore, we give an affirmative answer to this question for the first time.
Sandile S. Motsa - One of the best experts on this subject based on the ideXlab platform.
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Spectral Relaxation Method and Spectral Quasilinearization Method for Solving Unsteady Boundary Layer Flow Problems
Advances in Mathematical Physics, 2014Co-Authors: Sandile S. Motsa, P. G. Dlamini, M. KhumaloAbstract:Nonlinear partial differential equations (PDEs) modelling unsteady boundary-layer flows are solved by the spectral Relaxation Method (SRM) and the spectral quasilinearization Method (SQLM). The SRM and SQLM are Chebyshev pseudospectral based Methods that have been successfully used to solve nonlinear boundary layer flow problems described by systems of ordinary differential equations. In this paper application of these Methods is extended, for the first time, to systems of nonlinear PDEs that model unsteady boundary layer flow. The new extension is tested on two problems: boundary layer flow caused by an impulsively stretching plate and a coupled four-equation system that models the problem of unsteady MHD flow and mass transfer in a porous space. Numerous simulation experiments are conducted to determine the accuracy and compare the computational performance of the proposed Methods against the popular Keller-box finite difference scheme which is widely accepted as being one of the ideal tools for solving nonlinear PDEs that model boundary layer flow problems. The results indicate that the Methods are more efficient in terms of computational accuracy and speed compared with the Keller-box.
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A spectral Relaxation Method for thermal dispersion and radiation effects in a nanofluid flow
Boundary Value Problems, 2013Co-Authors: Peri K. Kameswaran, Precious Sibanda, Sandile S. MotsaAbstract:In this study we use a new spectral Relaxation Method to investigate heat transfer in a nanofluid flow over an unsteady stretching sheet with thermal dispersion and radiation. Three water-based nanofluids containing copper oxide CuO, aluminium oxide Al2O3 and titanium dioxide TiO2 nanoparticles are considered in this study. The transformed governing system of nonlinear differential equations was solved numerically using the spectral Relaxation Method that has been proposed for the solution of nonlinear boundary layer equations. Results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity, temperature and nanoparticle fraction profiles for some values of the governing physical and fluid parameters. Validation of the results was achieved by comparison with limiting cases from previous studies in the literature. We show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to common numerical Methods for solving nonlinear boundary value problems. We show that the convergence rate of the spectral Relaxation Method is significantly improved by using the Method in conjunction with the successive over-Relaxation Method.
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Solving Hyperchaotic Systems Using the Spectral Relaxation Method
Abstract and Applied Analysis, 2012Co-Authors: Sandile S. Motsa, P. G. Dlamini, M. KhumaloAbstract:A new multistage numerical Method based on blending a Gauss-Siedel Relaxation Method and Chebyshev pseudospectral Method, for solving complex dynamical systems exhibiting hyperchaotic behavior, is presented. The proposed Method, called the multistage spectral Relaxation Method (MSRM), is applied for the numerical solution of three hyperchaotic systems, namely, the Chua, Chen, and Rabinovich-Fabrikant systems. To demonstrate the performance of the Method, results are presented in tables and diagrams and compared to results obtained using a Runge-Kutta-(4,5)-based MATLAB solver, ode45, and other previously published results.
Hajime Okumura - One of the best experts on this subject based on the ideXlab platform.
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threshold voltage instability in 4h sic mosfets with nitrided gate oxide revealed by non Relaxation Method
Japanese Journal of Applied Physics, 2016Co-Authors: Mitsuru Sometani, Dai Okamoto, Shinsuke Harada, Hitoshi Ishimori, Shinji Takasu, Tetsuo Hatakeyama, Manabu Takei, Yoshiyuki Yonezawa, Kenji Fukuda, Hajime OkumuraAbstract:The threshold-voltage (V th) shift of 4H-SiC MOSFETs with Ar or N2O post-oxidation annealing (POA) was measured by conventional sweep and non-Relaxation Methods. Although the V th shift values of both samples were almost identical when measured by the sweep Method, those for the Ar POA samples were larger than those for the N2O POA samples when measured by the non-Relaxation Method. Thus, we can say that investigating the exact V th shifts using only the conventional sweep Method is difficult. The temperature-dependent analysis of the V th shifts measured by both Methods revealed that the N2O POA decreases charge trapping in the near-interface region of the SiO2.
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Exact Characterization of Threshold Voltage Instability in 4H-SiC MOSFETs by Non-Relaxation Method
Materials Science Forum, 2015Co-Authors: Mitsuru Sometani, Dai Okamoto, Shinsuke Harada, Hitoshi Ishimori, Shinji Takasu, Tetsuo Hatakeyama, Manabu Takei, Yoshiyuki Yonezawa, Kenji Fukuda, Hajime OkumuraAbstract:In this work, we investigated the Methods that measure the threshold voltage (Vth) instability without Relaxation of the gate stress during the Vth measurement. We propose a non-Relaxation Method that demonstrates exact Vth shifts compared with conventional Methods that are not as accurate. In the non-Relaxation Method, the constant gate-source voltage (Vgs) is continuously applied as a gate stress while the drain voltage (Vds) shift required to maintain a constant drain current (Id) is measured. Then, the Vds shift is converted to a Vth shift. The Vth shift values measured by the non-Relaxation Method are larger than those measured by the other Methods, which means that the non-Relaxation Method can very accurately measure the Vth shift.
M. Khumalo - One of the best experts on this subject based on the ideXlab platform.
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Spectral Relaxation Method and Spectral Quasilinearization Method for Solving Unsteady Boundary Layer Flow Problems
Advances in Mathematical Physics, 2014Co-Authors: Sandile S. Motsa, P. G. Dlamini, M. KhumaloAbstract:Nonlinear partial differential equations (PDEs) modelling unsteady boundary-layer flows are solved by the spectral Relaxation Method (SRM) and the spectral quasilinearization Method (SQLM). The SRM and SQLM are Chebyshev pseudospectral based Methods that have been successfully used to solve nonlinear boundary layer flow problems described by systems of ordinary differential equations. In this paper application of these Methods is extended, for the first time, to systems of nonlinear PDEs that model unsteady boundary layer flow. The new extension is tested on two problems: boundary layer flow caused by an impulsively stretching plate and a coupled four-equation system that models the problem of unsteady MHD flow and mass transfer in a porous space. Numerous simulation experiments are conducted to determine the accuracy and compare the computational performance of the proposed Methods against the popular Keller-box finite difference scheme which is widely accepted as being one of the ideal tools for solving nonlinear PDEs that model boundary layer flow problems. The results indicate that the Methods are more efficient in terms of computational accuracy and speed compared with the Keller-box.
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Solving Hyperchaotic Systems Using the Spectral Relaxation Method
Abstract and Applied Analysis, 2012Co-Authors: Sandile S. Motsa, P. G. Dlamini, M. KhumaloAbstract:A new multistage numerical Method based on blending a Gauss-Siedel Relaxation Method and Chebyshev pseudospectral Method, for solving complex dynamical systems exhibiting hyperchaotic behavior, is presented. The proposed Method, called the multistage spectral Relaxation Method (MSRM), is applied for the numerical solution of three hyperchaotic systems, namely, the Chua, Chen, and Rabinovich-Fabrikant systems. To demonstrate the performance of the Method, results are presented in tables and diagrams and compared to results obtained using a Runge-Kutta-(4,5)-based MATLAB solver, ode45, and other previously published results.
Susumu Yamashiro - One of the best experts on this subject based on the ideXlab platform.
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Unit commitment scheduling by Lagrange Relaxation Method taking into account transmission losses
Electrical Engineering in Japan, 2005Co-Authors: Daisuke Murata, Susumu YamashiroAbstract:Since the application of the Lagrange Relaxation Method to the unit commitment scheduling by Muckstadt in 1979, many papers using this Method have been published. The greatest advantage of applying the Lagrange Relaxation Method for the unit commitment problem is that it can relax (ignore) each generator's output dependency caused by the demand–supply balance constraint so that a unit commitment of each generator is determined independently by dynamic programming. However, when we introduce the transmission loss into the demand–supply balance constraint, we cannot decompose the problem into the partial problems in which each generator's unit commitment is determined independently and have to take some measures to obtain an optimal schedule by the Lagrange Relaxation Method directly. In this paper, we present an algorithm for the unit commitment schedule using the Lagrange Relaxation Method for the case of taking into account transmission losses. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 152(4): 27–33, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20119
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Unit Commitment Scheduling by Lagrange Relaxation Method Taking into Account Transmission Losses
IEEJ Transactions on Power and Energy, 2004Co-Authors: Daisuke Murata, Susumu YamashiroAbstract:After the application of the Lagrange Relaxation Method to the unit commitment scheduling by Muckstadt in 1979, many papers using this Method have been reported so far. The greatest advantage of applying the Lagrange Relaxation Method for the unit commitment problem is that it can relax (ignore) each generator’s output dependency caused by demand-supply balance constraint so that an unit commitment of each generator is determined independently by Dynamic Programming. However, when we introduce the transmission loss into the demand-supply balance constraint, we cannot decompose the problem into the partial problems in which each generator’s unit commitment is determined independently and have to take some measures to get an optimal schedule by Lagrange Relaxation Method directly. In this paper, we present an algorithm for the unit commitment schedule using the Lagrange Relaxation Method for the case of taking into account transmission losses.
