This paper explores the effectiveness of the Lie derivative discretisation scheme applied to two particular types of nonlinear dynamical equations, both of which have the characteristic of time variables in the denomi...
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This paper explores the effectiveness of the Lie derivative discretisation scheme applied to two particular types of nonlinear dynamical equations, both of which have the characteristic of time variables in the denominator position. The discrete structure of non-autonomous systems is established. In particular, we exclude time variables as state variables to prevent non-autonomous systems from becoming autonomous systems. Using this method, we compute the numerical solution of the system above and compare it with the precise solution and the numerical findings of Runge-Kutta, demonstrating the broad applicability of the Lie derivative numerical algorithm. Finally, we determine the CPU consumption time of two numerical algorithms, thus providing evidence of the high efficiency of the Lie derivative numerical algorithm.
A method to analyse bifurcation points by establishing bifurcation equations and solving them with an asymptotic expansion method is presented. Bifurcation equations are obtained using a decomposition of the spaces by...
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A method to analyse bifurcation points by establishing bifurcation equations and solving them with an asymptotic expansion method is presented. Bifurcation equations are obtained using a decomposition of the spaces by means of the theory of Lyapunov-Schmidt. To solve these bifurcation equations, an asymptotic expansion along the lines of Koiter is applied. The expansion is presented in a form suited for implementation in a finite element context. It is easy to extend the expansion to higher order terms in order to increase the accuracy. The accuracy of the method is verified with two examples. (C) 2000 Elsevier Science Ltd. All rights reserved.
This paper consider the pointwise controls problem of Hopfield neural network equation with diffusion term subject to quadratic criteria in the framework of variational method. Based on established optimal control the...
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This paper consider the pointwise controls problem of Hopfield neural network equation with diffusion term subject to quadratic criteria in the framework of variational method. Based on established optimal control theory to pointwise case, numerical study is carried out by constructing a semi-discrete algorithm with continuous time. Furthermore, for given point control inputs, the optimal pointwise controls are obtained to achieve the minimization. Experiments demonstration is implemented for verifying proposed algorithm. (C) 2008 Elsevier Inc. All rights reserved.
We present an innovative approach for solving time dependent Four Dimensional Variational Data Assimilation (4D VAR DA) problems. The proposed approach performs a decomposition of the whole physical domain, i.e. both ...
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We present an innovative approach for solving time dependent Four Dimensional Variational Data Assimilation (4D VAR DA) problems. The proposed approach performs a decomposition of the whole physical domain, i.e. both along spatial and temporal directions;a reduction in space and time of both the Partial Differential Equations-based model and the Data Assimilation functional;finally it uses a modified regularization functional describing restricted 4D VAR DA problems on the domain decomposition. Innovation mainly lies in the introduction ab initio, i.e. on the numerical model - of a domain decomposition approach in space and time joining the idea of Schwarz's method and Parallel in Time (PinT)-based approaches. We provide the numerical framework of this method including convergence analysis and error propagation. A validation analysis is performed discussing computational results on a case study relying on Shallow Water Equations. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
The numerical solution of the nonlinear heat conduction equation is used to analyze nonlinear effects in the laser. ash method, when the thermophysical parameters of the sample depend on the temperature. A parameter e...
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The numerical solution of the nonlinear heat conduction equation is used to analyze nonlinear effects in the laser. ash method, when the thermophysical parameters of the sample depend on the temperature. A parameter estimation technique is proposed to determine the temperature dependence of the thermal diffusivity from a response curve. Computer generated data, as well as real experimental data, were used to demonstrate the reliability of the technique.
In this paper the fractional oscillator equation in a finite time interval is considered. The fractional equation with derivatives of order (0,1] is transformed into its corresponding integral form, by using the symbo...
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In this paper the fractional oscillator equation in a finite time interval is considered. The fractional equation with derivatives of order (0,1] is transformed into its corresponding integral form, by using the symbolic calculus method, in which the binomial expansion of the inverse integral operator is used. A new fractional integral operator is introduced. A numerical algorithm to approximate the solution of the considered equation is proposed. In the final part of this paper examples of numerical solutions of this equation are given.
Model M7f is a new model for fiber reinforced concretes under static and dynamic loads, which features two kinds of improvement over the earlier versions: (I) It is built on M7, a new, greatly improved, microplane mod...
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Model M7f is a new model for fiber reinforced concretes under static and dynamic loads, which features two kinds of improvement over the earlier versions: (I) It is built on M7, a new, greatly improved, microplane model for plain concrete;and (2) it includes a more realistic description of the fiber pullout and breakage. The former include: (a) the absence of volumetric deviatoric split of elastic strains, which eliminates excessive lateral expansions or contractions and stress locking in far post-peak extensions;(b) simulation of the differences between hydrostatic compression and uniaxial compression under rigid lateral confinement;and (c) high shear dilatancy of low strength concretes;and realistic description of unloading, reloading and load cycles, even if they cross between tension and compression. The latter includes an improved continuous dependence of the effect of fibers on the fiber volume fraction. The fiber resistance is a function of the strain representing the average opening of cracks of given spacing and, as in model M5f, a horizontal plateau as a function of the type of fiber and fiber volume fraction has been employed and used systematically for all fits. In this study, this horizontal plateau is justified using uniformly distributed crack bridging fibers. The model behavior is calibrated and verified by fitting of the main test data from the literature. The match of experimental observations and the computational results is closer than in the previous models. (C) 2013 Elsevier Ltd. All rights reserved.
A simple method for computing the strain and the time dependent constants for non-linear viscoelastic materials is presented. The method is based on the finite time increment formulation of the convolution integral, a...
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A simple method for computing the strain and the time dependent constants for non-linear viscoelastic materials is presented. The method is based on the finite time increment formulation of the convolution integral, and is applicable for materials which exhibit separable strain and time variables. The strain-dependent function can take any form including the hyperelastic potentials such as the Mooney-Rivlin strain energy function. The time-dependent function is based on the Prony series. The attraction of the method is that true material constants can be computed for any deformation history.
Purpose-The purpose of this paper is to study the parameter estimation problem of nonlinear multivariable output error moving average systems. Design/methodology/approach-A partially coupled extended stochastic gradie...
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Purpose-The purpose of this paper is to study the parameter estimation problem of nonlinear multivariable output error moving average systems. Design/methodology/approach-A partially coupled extended stochastic gradient algorithm is presented for nonlinear multivariable systems by using the decomposition technique. Findings-The proposed algorithm can realize the coupled computation of the parameter estimates between subsystems. Originality/value-This paper develops a coupled parameter estimation algorithm for nonlinear multivariable systems and directly estimates the system parameters without over-parameterization.
The Internet traffic analysis is important to network management, and extracting the baseline traffic patterns is especially helpful for some significant network applications. In this paper, we study on the baseline p...
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The Internet traffic analysis is important to network management, and extracting the baseline traffic patterns is especially helpful for some significant network applications. In this paper, we study on the baseline problem of the traffic matrix satisfying a refined traffic matrix decomposition model, since this model extends the assumption of the baseline traffic component to characterize its smoothness, and is more realistic than the existing traffic matrix models. We develop a novel baseline scheme, named Stable Principal Component Pursuit with Time-Frequency Constraints (SPCP-TFC), which extends the Stable Principal Component Pursuit (SPCP) by applying new time-frequency constraints. Then we design an efficient numerical algorithm for SPCP-TFC. At last, we evaluate this baseline scheme through simulations, and show it has superior performance than the existing baseline schemes RBL and PCA. (C) 2014 Elsevier GmbH. All rights reserved.
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