Showing papers in "Communications in Nonlinear Science and Numerical Simulation in 1999"
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TL;DR: In this article, a linearized perturbation method is proposed to obtain the unperturbed equation by linearizing the original nonlinear equation, not by setting e = 0, and the obtained results are valid not only for small parameters, but also for very large values of e.
74 citations
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TL;DR: In this paper, an approximate analytical solution of Blasius equation is obtained by the parameter iteration method, and the comparison with Howarth's numerical solution shows that the accuracy of the proposed method is higher than other approximate analytical solutions.
35 citations
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TL;DR: A new model for the same problem is proposed and a comparison of simulation results with the former ones shows that the new model works better under the condition of high traffic density.
18 citations
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TL;DR: In this article, a difference scheme for the periodic initial-boundary problem of the coupled KdV Equation is given, which keeps the first two conserved quantities which the differential equation possesses.
18 citations
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TL;DR: In this article, Backlund transformation of (2+1)-dimensional Kolmogoroff Petrovsky-Piscounov (KPP) equation is derived via using the idea of improved homogeneous balance method and with the aid of MATHEMATICA.
17 citations
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TL;DR: In this article, a nonlinear oscillator with no possible small parameters is considered, and an approximate solution which is valid on the whole solution domain, and the results are in remarkable agreement with the exact one even in the case where the amplitude of the oscillator tends to infinite.
14 citations
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TL;DR: In this paper, the chaotic differential equation with impulse effect is introduced including its fundamental theory, and the theory of the dynamics is applied and the computer simulation is given for illustrating the chaotic characteristic of this kind of system.
14 citations
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TL;DR: Two types of symmetry reductions for the variable coefficient MKdV equation, which contain well-known Painleve II type equation and Jacobian elliptic equation, were derived in this paper.
14 citations
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TL;DR: Some typical results of computation on the shock (blast) wave interaction (2D and 3D) with bodies and its experimental validation in shock tube are summarized, suggestions for improving the numerical method (difference scheme and grid systems), developing 3-D optical quantitative visualization technology and further studying the unsteady turbulent flow are put forward as mentioned in this paper.
14 citations
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TL;DR: In this article, a new parameter iteration technique is proposed to solve the Duffing equation with strong and high order nonlinearity, which converges asymptotically to the exact result, not a constant.
12 citations
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TL;DR: This sufficient condition of the asymptotical stability of the zero solution about the nonautonomous equation d z d t = A(t)z + o(‖z‖) is presented and a new method without any limitation on the response system in the synchronization is proposed.
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TL;DR: In this paper, the authors apply a new asymptotic technique for nonlinear problems, namely the homotopy analysis method (HAM) proposed by LIAO, to give analytic solutions at the 10th-order approximation of the viscous flow past a sphere.
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TL;DR: In this article, the longitudinal vibrations of a rheological rod with variable cross-section are examined, and the eigenfunction of the solution is obtained for natural vibrations of the rod with hereditary material of standard hereditary body.
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TL;DR: In this paper, large eddy simulations of spatially evolved turbulent rounds jets were presented, and two SGS models called the standard Smagorinsky's eddy viscosity model and the non-eddy visco-ity stimulated small scale (SSSS) model developed by Shah & Ferziger[l] were applied.
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TL;DR: In this paper, the authors measured and analyzed void fraction waves in different flow regimes and showed that the propagation velocity of void fraction wave depends on the flow regime and the mean void fraction.
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TL;DR: In this article, an extension of the characteristic equation analysis method to the stability analysis of equilibrium points for closed-loop PWM power switching converters is introduced based on equivalent small parameter method.
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TL;DR: In this article, the existence and uniqueness of stationary solution a bipolar incompressible viscous fluids is established and it is also obtained that the every solution of the system converges to the stationary solution as time t → ∞.
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TL;DR: This paper derived the standard diffusion equation from the continuity equation and discussed the defectiveness of earlier proposed diffusion equations, and then derived the generalized fractional diffusion equation for anomalous diffusion, which is a generalized version of the diffusion equation.
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TL;DR: In this article, several kinds of explicit and exact solutions for the generalized reaction duffing equation are obtained by using a new ansatz, which contain new solitary wave solutions and period solutions.
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TL;DR: In this paper, a handy method of calculating the conditional Lyapunov exponents of differential dynamical systems and the conditional Lipschitz exponents can be acquired easily with the method, which has been successfully used in different kinds of synchronization, such as continuous driving synchronization, impulsive (sporadic) driving synchronization and intermittently driving synchronization.
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TL;DR: In this paper, the error of one-leg methods applied to differential-algebraic equations of index 2 in Hessenberg form was investigated and numerical examples in line with the theoretical results were included.
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TL;DR: In this article, a formulation on large eddy simulation with the idea motivated by Fourier series representation is presented, and a set of filtered equations are obtained, based on the Fourier-series representation.
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TL;DR: A nonlinear method named as “Complexity Analysis”, by which the chaotic and other behavior in heart rate of the patients suffer from AMI, STSDS and VPB, is introduced.
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TL;DR: In this article, the time evolution of a turbulent gravity current of lock release type, formed by a finite volume of homogeneous fluid released instantaneously into another fluid of slightly lower density, was studied numerically via the renormalization group (RNG) κ-ϵ model for Reynolds-stress closure to characterize the flow with transitional and highly localized turbulence.
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TL;DR: In this article, the necessary and sufficient conditions for the existence of periodic solutions of nonlinear impulsive differential systems were given by using a special function and study the stable properties of such solutions.
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TL;DR: In this article, a diffusion equation for disordered fractal media in three-dimensional case is derived from standard diffusion equation on fractals, and it includes literature result as a particular case.
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TL;DR: A neural network for solving monotone linear complementary problem is proposed and is proven to be uniformly, asymptotically and stably convergent to an exact solution of thelinear complementary problem.
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TL;DR: In this paper, the authors proved the global existence of solutions for a class of quasilinear parabolic systems with cross-diffusion effects and competition interaction on any smooth bounded domain in RN.
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TL;DR: In this paper, the authors show that the shearing stresses in curved beams can be solved explicitly from an integral equation, which is obtained by differentiation and integral manipulations, and two novel formulae for shearing and radial stresses are also presented.
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TL;DR: The result shows that the series of HRV have typical nonlinear character and the predictability can be a rather accurate parameter to analyze and diagnose cardiovascular diseases in clinics.