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1.
We use the implicit function theorem to prove an existence of a heteroclinic orbit to a system of two non-linear second-order ODEs. The perturbation is carried out around infinite value of a ‘coupling parameter’. The form of the system which is considered in this paper is related to the system defining travelling wave solutions in a two temperature model of the laser sustained plasma. 相似文献
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A reaction-diffusion system describing a simple activator-inhibitor reaction is investigated in the limiting case of “very large” diffusion rate of the inhibitor. Using singular perturbation techniques, an inner and an outer expansion are derived. The latter, describing the large-time behavior of the system, is governed by equations that, in the first orders of approximation, possess asymptotically stable space-inhomogeneous equilibria (patterns), and whose set of equilibria is globally attractive. 相似文献
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The paper deals with a class of ordinary differential systems which contains a differential inclusion describing input–output relations of hysteresis type. Existence and uniqueness of local and global solutions of the systems under consideration are proved. 相似文献
5.
《Applied Numerical Mathematics》1997,24(1):1-21
In this paper a new mesh selection strategy, based on the conditioning properties of continuous problems, is presented. It turns out to be particularly efficient when approximating solutions of BVPs. The numerical methods used to test the reliability of the strategy are symmetric Linear Multistep Formulae (LMF) used as Boundary Value Methods (BVMs) since they provide a wide choice of methods of arbitrary high order and have similar stability properties to each other. In particular, we shall consider a subclass of such methods, called Top Order Methods (TOMs) (Amodio, 1996; Brugnano and Trigiante, 1995, 1996), to carry out the numerical results on some singular perturbation test problems. 相似文献
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Hossein Aminikhah Jafar Biazar 《Numerical Methods for Partial Differential Equations》2010,26(5):1115-1124
In this article, a new homotopy perturbation method (NHPM) is introduced to obtain exact solutions of system of ODEs. Theoretical considerations are discussed. Comparison of the results of applying NHPM with those of homotopy perturbation method (HPM) and Adomia's decomposition method (ADM) leads to significant consequences. Three examples, including stiff system of linear and nonlinear ODEs are given to demonstrate the efficiency of the new method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
7.
有O初始条件的多级一阶线性常系数微分方程组,可以用拉氏变换求解,并且解还可以用Green矩阵来表达.早已为人所知.但关于Green矩阵的一个在实际中有用的表达形式,因为推导上有毛病,未被普遍接受.本文对此毛病作了点注记.予以克服. 相似文献
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This paper contains a study of a simple multirate scheme, consisting of the θ-method with one level of temporal local refinement. Issues of interest are local accuracy, propagation of interpolation errors and stability. The theoretical results are illustrated by numerical experiments, including results for more levels of refinement with automatic partitioning. 相似文献
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Djordjevic Jasmina Konjik Sanja Mitrović Darko Novak Andrej 《Journal of Optimization Theory and Applications》2021,190(1):316-338
Journal of Optimization Theory and Applications - We consider exact and averaged control problem for a system of quasilinear ODEs and SDEs with a nonnegative definite symmetric matrix of the... 相似文献
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We discuss the design of software that is easy to use for simple problems, but still capable of solving complicated problems. Nowadays a design should accommodate related, but fundamentally different, tasks such as solving DAEs and DDEs in addition to IVPs and BVPs for ODEs. Major issues are illustrated with the MATLAB ODE Suite and selected solvers written in Fortran 90 and Maple. 相似文献
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Franco Obersnel Pierpaolo Omari 《Proceedings of the American Mathematical Society》2007,135(7):2055-2058
We extend a result of J. Andres and K. Pastor concerning scalar time-periodic first order ordinary differential equations without uniqueness, by proving that the existence of just one subharmonic implies the existence of large sets of subharmonics of all given orders. Since these periodic solutions must coexist with complicated dynamics, we might paraphrase T. Y. Li and J. A. Yorke by loosely saying that in this setting even period two implies chaos. Similar results are obtained for a class of differential inclusions.
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Multirate time stepping is a numerical technique for efficiently solving large-scale ordinary differential equations (ODEs) with widely different time scales localized over the components. This technique enables one to use large time steps for slowly varying components, and small steps for rapidly varying ones. Multirate methods found in the literature are normally of low order, one or two. Focusing on stiff ODEs, in this paper we discuss the construction of a multirate method based on the fourth-order RODAS method. Special attention is paid to the treatment of the refinement interfaces with regard to the choice of the interpolant and the occurrence of order reduction. For stiff, linear systems containing a stiff source term, we propose modifications for the treatment of the source term which overcome order reduction originating from such terms and which we can implement in our multirate method. 相似文献
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Egon Balas 《Computational Optimization and Applications》1998,10(2):189-193
Projection of a polyhedron involves the use of a cone whose extreme rays induce the inequalities defining the projection. These inequalities need not be facet defining. We introduce a transformation that produces a cone whose extreme rays induce facets of the projection. 相似文献
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Yi Zhang Haifeng Huo Yinkang Xu Yinjie Lu 《Journal of Nonlinear Modeling and Analysis》2019,1(2):179-192
By virtue of the KP hierarchy reduction method, the N-dark soli-
ton solutions of the multi-component Maccari system are constructed. Taking
the coupled Maccari system for instance, the N-dark soliton solutions are fur-
ther obtained in terms of determinants. In addition, in contrast with bright-
bright soliton collisions, the dynamical analysis shows that the collisions of
dark-dark solitons are elastic and there is no energy exchange among soli-
tons in different components. What’s more, we also investigate the dark-dark
soliton bound states including stationary and moving ones. 相似文献
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Computational Mathematics and Mathematical Physics - The possibility of finding soliton solutions of a nonintegrable generalization of the coupled Volterra system is studied. This generalization is... 相似文献
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G. Beylkin M.E. Brewster A.C. Gilbert 《Applied and Computational Harmonic Analysis》1998,5(4):450-486
The multiresolution analysis (MRA) strategy for the reduction of a nonlinear differential equation is a procedure for constructing an equation directly for the coarse scale component of the solution. The MRA homogenization process is a method for building a simpler equation whose solution has the same coarse behavior as the solution to a more complex equation. We present two multiresolution reduction methods for nonlinear differential equations: a numerical procedure and an analytic method. We also discuss one possible appproach to the homogenization method. 相似文献
18.
本文应用比较定理研究了一类非线性边界条件的向量非线性奇摄动问题εx='f(t,x,y,e)εy'=g(t,x,y,ε)x(0)=A(ξ1,ξ2,x(1)-x(0),y(1)-y(0),ε)y(0)=B(ξ1,ξ,x(1)-x(0),y(1)-y(0),ε)这里ξ1,ξ2为ε的函数。0<ε<<1,在适当的条件下,作出了任意次精度的渐近展式。并得出余项估计。 相似文献
19.
Computational Mathematics and Mathematical Physics - A perturbed Hamiltonian system with a time-independent unperturbed part and a time-periodic perturbation is considered near a stationary... 相似文献
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Jan Andres Tomá s Fü rst Karel Pastor 《Proceedings of the American Mathematical Society》2007,135(10):3187-3191
We present an elementary proof that, for a multivalued map with nonempty connected values and monotone margins, the existence of a periodic orbit of any order implies the existence of periodic orbits of all orders. This generalizes a very recent result of this type in terms of scalar ordinary differential equations without uniqueness, due to F. Obersnel and P. Omari, obtained by means of lower and upper solutions techniques.