共查询到20条相似文献,搜索用时 15 毫秒
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Brian A. Coomes 《Transactions of the American Mathematical Society》1997,349(1):203-216
A finite time shadowing theorem for autonomous ordinary differential equations is presented. Under consideration is the case were there exists a twice continuously differentiable function mapping phase space into with the property that for a particular regular value of the submanifold is invariant under the flow. The main theorem gives a condition which implies that an approximate solution lying close to is uniformly close to a true solution lying in . Applications of this theorem to computer generated approximate orbits are discussed.
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Hossein Aminikhah Jafar Biazar 《Numerical Methods for Partial Differential Equations》2010,26(2):480-489
In this paper, we introduce a new version of the homotopy perturbation method (NHPM) that efficiently solves linear and non‐linear ordinary differential equations. Several examples, including Euler‐Lagrange, Bernoulli and Ricatti differential equations, are given to demonstrate the efficiency of the new method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
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Dr. D. P. Squier 《Numerische Mathematik》1969,13(2):176-179
Summary It is proved that any consistent one-step method for solving the initial value problem for a first-order ordinary differential equation is convergent; no stability condition is required. An application is made to a similarly stated result, allowing part of the hypothesis in that case to be dropped. 相似文献
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Josef Kalas 《Czechoslovak Mathematical Journal》1998,48(2):373-384
In the present paper we give general nonuniqueness results which cover most of the known nonuniqueness criteria. In particular, we obtain a generalization of the nonuniqueness theorem of CHR. NOWAK, of SAMIMI's nonuniqueness theorem and of STETTNER's nonuniqueness criterion. 相似文献
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E. L. Perchik 《Ukrainian Mathematical Journal》1995,47(9):1427-1434
We present a method for the solution of nonlinear second-order differential equations by using a system of Fredholm equations of the second kind.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 9, pp. 1254–1260, September, 1995. 相似文献
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A maximum principle is obtained for solutions of fourth order ordinary differential equations. As an application, the existence of a nonnegative (positive) solution of a nonlinear boundary problem is established. Extension of the maximum principle for solutions of higher order equations is also indicated. 相似文献
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Philip Korman 《Applicable analysis》2013,92(3-4):267-273
We present a maximum principle for fourth order ordinary differential equations, based on a new approach involving counting of inflection points. We use our results to compute solutions of nonlinear equations describing static displacements of a uniform beam 相似文献
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Desjardins Benoit 《偏微分方程通讯》2013,38(11-12):1667-1703
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H. B. Thompson 《Applicable analysis》2013,92(1-2):27-43
Explicit upper and lower bounds are constructed for a functional defined on the difference of solutions to a class of nonlinear hyperbolic problems modelling string vibrations. Such bounds indicate how solutions are affected by the input data over a finite time interval. The logarithmic convexity method is used to obtain two second order ordinary differential inequalities for the appropriate functional. These inequalities are then related to two systems of first order equations whose solutions are the desired bounds. 相似文献
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Boundary value methods for solving ordinary differential equations require the solution of non-symmetric, large and sparse linear systems. In this paper, these systems are solved by using the generalized minimal residual (GMRES) method. A circulant-block preconditioner is proposed to speed up the convergence rate of the GMRES method. Theoretical and practical arguments are given to show that this preconditioner is more efficient than some other circulant-type preconditioners in some cases. A class of waveform relaxation methods is also proposed to solve the linear systems. 相似文献
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This paper generalizes various uniqueness results and offers very general uniqueness criteria which include different types of results considered so far. 相似文献
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Markus Kirkilionis 《Journal of Mathematical Analysis and Applications》2004,299(1):157-173
We state and prove general comparison principles for ordinary differential equations, discuss the scope of these principles, and present examples. 相似文献