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1.
Stochastic ordinary differential equations are investigated for which the coefficients depend on nonlocal properties of the current random variable in the sample space such as the expected value or the second moment. The approach here covers a broad class of functional dependence of the right-hand side on the current random state and is not restricted to pathwise relations. Existence and uniqueness of solutions is obtained as a limiting process by freezing the coefficients over short time intervals and applying existence and uniqueness results and appropriate estimates for stochastic ordinary differential equations.  相似文献   

2.
For higher order ordinary differential equations, new sufficient conditions on the existence and uniqueness of periodic solutions are established. Results obtained cover the case when the right-hand side of the equation is not of a constant sign with respect to an independent variable.  相似文献   

3.
For higher order ordinary differential equations, new sufficient conditions on the existence and uniqueness of periodic solutions are established. Results obtained cover the case when the right-hand side of the equation is not of a constant sign with respect to an independent variable.  相似文献   

4.
A family of two-sided Runge—Kutta formulas accurate to sixth order is constructed for numerical solution of the Cauchy problem for second-order ordinary differential equations, which are solved for the highest derivative and have a sufficiently smooth right-hand side. Two-sided approximations to the sought solution are obtained after up to nine evaluations of the right-hand side of the differential equation in each integration step. The efficiency of the proposed formula is demonstrated in application to two test examples.Sumy Teachers' College. Kiev Teachers' College. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 68, pp. 45–51, 1989.  相似文献   

5.
Yevstafyeva  V. V. 《Mathematical Notes》2021,109(3-4):551-562
Mathematical Notes - A system of $$n$$ th-order ordinary differential equations with relay nonlinearity and periodic perturbation function on the right-hand side is studied. The matrix of the...  相似文献   

6.
When the finite-difference method is used to solve initial- or boundary value problems with smooth data functions, the accuracy of the numerical results may be considerably improved by acceleration techniques like Richardson extrapolation. However, the success of such a technique is doubtful in cases were the right-hand side or the coefficients of the equation are not sufficiently smooth, because the validity of an asymptotic error expansion — which is the theoretical prerequisite for the convergence analysis of the Richardson extrapolation — is not a priori obvious. In this work we show that the Richardson extrapolation may be successfully applied to the finite-difference solutions of boundary value problems for ordinary second-order linear differential equations with a nonregular right-hand side. We present some numerical results confirming our conclusions.  相似文献   

7.
We introduce measure functional differential equations with infinite delay and an axiomatically described phase space. We show how to transform these equations into generalized ordinary differential equations whose solutions take values in a suitable infinite-dimensional Banach space. Even in the special case of functional equations with finite delay, our result improves the existing one by imposing weaker conditions on the right-hand side.  相似文献   

8.
We study problem of global classification of ordinary differential equations with the linear-fractional right-hand side with rational coefficients with respect to a symmetry group. We find the field of differential invariants and obtain the equivalence criterion for two such equations. We adduce certain examples for applying of this criterion. These examples were obtained by means of computer.  相似文献   

9.
In this paper we obtain, as an application of a Darbo-type theorem, global solutions for differential equations with impulse effects, under the assumption that the function on the right-hand side is integrable in the Henstock sense. We thus generalize several previously given results in literature, for ordinary or impulsive equations.  相似文献   

10.
In this paper, the control parametrization enhancing technique (CPET) is applied to obtain numerical solution to a special class of ordinary differential equations where the right-hand side has state dependent discontinuities. Switching locations corresponding to these discontinuities can be calculated exactly and conveniently. Illustrative examples are provided to demonstrate the novel technique.  相似文献   

11.
For nonlinear ordinary differential equations of the second order with a derivative on the right-hand side and boundary conditions of the first kind, we construct and justify generalized three-point difference schemes of high order of accuracy on a nonuniform mesh. The existence and uniqueness of their solutions are proved, and an a priori estimate of the accuracy is obtained.  相似文献   

12.
We consider a time-invariant, finite-dimensional system of ordinary differential equations, whose right-hand side is continuous, but not Lipschitz continuous in general. For such a system, stability cannot be characterized in general by means of smooth Liapunov functions. We prove a new version of the converse of first Liapunov theorem. We give also some new conditions which allow us to verify, in different circumstances, whether a nonsmooth function is monotone along the solutions of the system.  相似文献   

13.
An algorithm convenient for numerical implementation is proposed for constructing differentiable control functions that transfer a wide class of nonlinear nonstationary systems of ordinary differential equations from an initial state to a given point of the phase space. Constructive sufficient conditions imposed on the right-hand side of the controlled system are obtained under which this transfer is possible. The control of a robotic manipulator is considered, and its numerical simulation is performed.  相似文献   

14.
The sufficient conditions of the sign determinacy of a sum of polylinear forms are obtained. From these systems the Lyapunov functions which are used to derive the sufficient conditions of the global asymptotic stability of the non-perturbed motion of non-linear systems are set up. At the same time the perturbed motion is described by a set of ordinary differential equations with the right-hand side in the form of the sum of homogeneous polynomials. An application to the analysis of the stability of winged aircraft is considered.  相似文献   

15.
In the paper methods from the theory of extensions of dynamical systems are used to studyβ-differential equations whose solutions possess the uniqueness property and depend continuously on the initial data and on the right-hand side of the equation. The Zhikov-Bronshtein theorems concerning asymptotically almost periodic solutions of ordinary differential equations are extended toβ-differential equations (in particular, to total differential equations). Along with asymptotic almost periodicity, we also consider asymptotic recurrence, weak asymptotic distality, and asymptotic distality. To the equations we associate dynamical systems generated by the space of the right-hand sides and the spaces of the solutions and of the initial data of solutions of the equation. Generally, the phase semigroups of the dynamical systems are not locally compact. Translated fromMatermaticheskie Zametki, Vol. 67, No. 6, pp. 837–851, June, 2000.  相似文献   

16.
A fixed mesh variational formulation is used to establish existence and uniqueness of the solution of ordinary differential equations with (infinitely many) state-dependent impulses on the right-hand side. This approach gives a natural numerical scheme to approximate the solution. The convergence of the approximation is proved and its asymptotic order obtained.  相似文献   

17.
In this paper we consider the optimal control problem for a system of first-order hyperbolic equations. The right-hand side of this system is determined by a control system of ordinary differential equations. Admissible controls belong to the class of smooth functions. We obtain an optimality condition and propose a general scheme of improvement methods for the mentioned problem.  相似文献   

18.
Parabolic initial boundary-value problems coupled (via the boundary condition) with ordinary differential equations whose right-hand side contains the Preisach hysteresis operator are considered. In particular, these problems model thermocontrol processes in chemical reactors, climate-control systems, biological cells, etc. For the Preisach operator with and without time delay, solvability, periodicity of solutions, and global B-attractors are studied.  相似文献   

19.
We prove a theorem stating that the uniform attractors of a family of semiprocesses that do not necessarily have a common time semigroup depend on the parameter uppersemicontinuously. We consider an explicit finite-difference scheme for a nonautonomous system of ordinary differential equations and an explicit spectral-difference scheme for the vorticity equation with time-dependent bounded right-hand side on a sphere. We obtain theorems on the existence of uniform attractors of numerical schemes and their closeness to true attractors of the original differential problems.  相似文献   

20.
Differential Equations - For autonomous systems of ordinary differential equations with fractional-rational right-hand sides for which the nonnegative orthant is positively invariant, sufficient...  相似文献   

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