Showing papers in "Communications in Nonlinear Science and Numerical Simulation in 1998"

TL;DR: In this article, a homotopy perturbation method with an imbedding parameter is proposed, which can take full advantage of the traditional perturbations methods and the hom-otopy technique.

TL;DR: In this article, an approximate analytical solution is obtained via the variational iteration method for the Blasius' equation, with boundary conditions, and the comparison with Howarth's numerical solution reveals that the proposed method is of high accuracy.

TL;DR: In this article, a Newton-like iteration method is proposed to solve an approximate solution of an algebraic equation and the iteration formula obtained by homotopy perturbation method contains the well-known Newton iteration formula in logic.

TL;DR: In this article, a homotopy analysis method is applied to give an explicit, totally analytic solution of the Blasius' flow, i.e. the two dimensional (2D) laminar viscous flow over a semi-infinite flat plate.

TL;DR: In this article, the synchronization of coupled dynamical systems is studied by means of differential inequality and Lyapunov's direct method, and the results are proved using differential inequality.

TL;DR: In this paper, a mixed finite element method for second order nonlinear hyperbolic equations is presented and improved L2-error estimates are established, where the convergence of both the function value and the flux is demonstrated.

TL;DR: In this paper, the effects of certain limiters used in TVD-type of schemes on the resolution of of numerical computations in hypersonic flows are investigated, and an explicit TVD scheme of Hasten-Yee type with velocity-dependent entropy correction function is employed in the computations.

TL;DR: This paper presents an exact method for evaluating connection coefficients on an interval, which can be used to solve PDEs numerically by the wavelet-Galerkin method.

TL;DR: An improved strategy in synchronization of chaotic dynamics as contrasted with PC(L.Pecora and T.Carroll) method and KSC(Kocarev L, Shang A, Chua,L.O.) control idea is presented.

TL;DR: In this article, superconvergence results for mixed finite element methods for second order nonlinear hyperbolic equations were derived for both the solution and gradients on the rectangular domain.

TL;DR: In this paper, a kinematics limit analysis for assessing the safety of slope or its critical slip surface is presented, and the searched slip surface with that by limit analysis is compared.

TL;DR: In this paper, a nonlinear Fokker-planck equation with a nonnegative Radon measure as its initial condition is studied and properties of the solutions have been obtained.

TL;DR: In this paper, the authors dealt with the initial-oblique derivative problem for nonlinear and nondivergence uniformly parabolic equations of the second order with measurable coefficients and proved the existence and uniqueness of solutions for the problem.

TL;DR: In this article, a general boundary element method (BEM) approach was proposed to overcome the limitations and restrictions of the traditional BEM approach for strongly nonlinear problems whose governing equations don't contain any linear terms.

TL;DR: In this paper, a method for determining the fixed point's neighborhood in which the system remain stable when subjected to a linear law is proposed, and the validity of this method is shown by a theorem on effective local control of nonlinear, chaotic dynamical system, with numerical confirmation.

TL;DR: The improved closed-loop control method is used to realize that the discrete chaotic system stabilizes to any arbitrarily chosen dynamics and the Henon system is chosen for an example.

TL;DR: In this paper, the structure of the strange attractors in the Lozi map is investigated on the basis of the results obtained by the authors in 1991-1993, which show that our viewpoint is correct.

TL;DR: In this paper, a generalized variational principle of classical type (not Curtin-type & not involving convolutions) for the entitled problem of linear anisotropic materials has been obtained directly from the field equations & boundary conditions.

TL;DR: In this paper, the derivatives and integrals on a fractal set contained in R were studied and the classical concepts and definitions of derivatives were naturally extended to this fractal case.

TL;DR: The existence of global attractors of the periodic initial value problem for the Ginzburg-Landau equations coupling with BBM equations was proved in this paper, and the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractor by means of uniformly a priori estimates for time were also obtained.

TL;DR: In this paper, an asymptotic gas magnetohydrodynamic system is formulated in variational principles via the semi-inverse method proposed by He, and a new theoretical basis for the finite element method is founded.

TL;DR: In this paper, a priori scale information about the model is used to constrain the inversion of the acoustic impedance model, and the wavelet transform is applied to reconstruct the model.

TL;DR: The results show that this new method can catch much more dynamical behavior of nonlinear PDE systems than the usual methods.

TL;DR: In this paper, a variational principle is established for a system of two conservation laws which is strictly hyperbolic, and applying variational technique with variable-domain, the Rankine-Hugoniot jump relations can be readily obtained as natural conditions.

TL;DR: In this paper, the authors clarified the misuse of Routh-Hurwitz criterion in judging the synchronization of the controlled nonlinear system and desired dynamics during the course of applying the control method which Jackson etc. had introduced and established their theory as well as corresponding criterion.

TL;DR: In this article, the authors used a Beam-Warming implicit algorithm to solve the Navier-Stokes equations of a 76° sweep delta wing at 36.5° angle of attack.

TL;DR: In this article, a method for determining the neighborhood of a period-T point in which the system remains stable when subjected to a linear feedback control is presented, and a theorem on the existence of neighborhood is rigorously proved using idea from functional analysis and polar coordinate transformation.

TL;DR: In this article, exact and explicit solitary wave solutions for the coupled nonlinear equation were obtained by using a simple way of making the ansatz u(χ, t) = Asechn + A0 with = k( χ + wt) + 0.

TL;DR: This paper considers the flow between two concentric rotating spheres, and combines the Legendre-Galerkin spectral methods in Part I together with the nonlinear Galerkin method, then constructs the full discrete nonlinear Legendre/Galerkins spectral scheme, and derives the stability conditions and its error estimate.

TL;DR: In this article, the existence of homoclinic orbits for perturbed nonlinear Schrodinger equation with five degree term under even periodic boundary conditions is considered. But the existence is not established for the truncation equation.