Ordinary Differential Equations
نویسنده
چکیده
subject to the constraint that q(0) and q(h) are constant. Standard ODE theory provides existence and uniqueness of the corresponding initial value problem because the derivatives q~(t) of the evolution curves q(t) are the integral curves of the corresponding Lagrangian vector field XE. Given two nearby ql, q2 6 Q, does there exist a unique evolution curve q(t) such that q(0) = q~ and q(h) = q2? This local boundary value problem occurs, for example, in the following two contexts: 1. If Q is a Riemannian manifold with metric g, and L(v) = lg (v ,v ) , then the Lagrangian evolution curves are constant-speed reparameterizations of the geodesics, and the local boundary value problem becomes that of locating the unique local geodesic connecting two sufficiently nearby points. 2. Type 1 generating functions St(q2, ql) for the Hamiltonian flow are defined by
منابع مشابه
APPLICATION NEURAL NETWORK TO SOLVE ORDINARY DIFFERENTIAL EQUATIONS
In this paper, we introduce a hybrid approach based on neural network and optimization teqnique to solve ordinary differential equation. In proposed model we use heyperbolic secont transformation function in hiden layer of neural network part and bfgs teqnique in optimization part. In comparison with existing similar neural networks proposed model provides solutions with high accuracy. Numerica...
متن کاملModified Laplace Decomposition Method for Singular IVPs in the second-Order Ordinary Differential Equations
In this paper, we use modified Laplace decomposition method to solving initial value problems (IVP) of the second order ordinary differential equations. Theproposed method can be applied to linear and nonlinearproblems
متن کاملViewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials
In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.
متن کاملReduction of Differential Equations by Lie Algebra of Symmetries
The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...
متن کاملNumerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type
In this paper, we have proposed a numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided in...
متن کاملStudy on usage of Elzaki transform for the ordinary differential equations with non-constant coefficients
Although Elzaki transform is stronger than Sumudu and Laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. In this paper, a method is introduced to find that a differential equation by Elzaki transform can be solved?
متن کامل