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In this paper, consider the following differential equations cycle: where x (t) = (x 1 (t), ..., x 2 (t)) T is a real-valued vector function R n , t is the time variable, T is the smallest positive cycle, f (t, x (t)) [0, T] × R n continuous vector-valued function. Assume that the problem (1) cycle solution exists and is stable under the premise to explore a numerical method. Initial value is not certainty can not be directly used to solve initial value problem of ordinary differential equations method to solve the problem of the numerical solution of differential equations cycle, so the value of the cycle problem solving difficulties. ODEs with numerical method for the development of more mature and perfect example Euler method, Runge-Kutta method, this paper, by introducing a reference variable ξ Order Periodic Boundary Value Problems with parameters translate into initial value problem, the choice of the initial value problem and the optimal parameters to achieve the purpose of solving the periodic solution. The procedure is as follows: First, the system (1) we introduce parametric The Xi into the problem (1): The Xi = (zeta 1 , the zeta 2 , ... , ξ n ) T ∈ R n . Define the objective function: J (The Xi) = 1/2 ‖ x (T)-zeta ‖ 2 (3) define the optimal parameters (P): For the system (2) to find of a system the parameters zeta ∈ R n , the objective function (3) reaches a minimum. Optimal parameter selection problem can be regarded as a nonlinear programming problem by calculating the gradient of the objective function, the optimal parameter selection problem into a mathematical programming problem, the use of existing mathematical programming techniques to solve. The thesis focuses on the cycle known and unknown two cases, the corresponding algorithm is given. Meanwhile, the paper also discusses the calculation of the pulse period differential system, as when the state x (t) is not a continuous process, can not be solved through the usual method. By introducing the transformation y i (S) = x (t i-1 (the t i for t i-1 ) s), 0 ≤ s ≤ 1, i = 1,2, ..., N. > * ∈ R n , such that (?) (The Xi) = 1/2 ‖ y in N (1)-zeta ‖ 2 in zeta * the ∈ the R n at the minimum, ie (?) the (zeta * ) ≤ (?) (The Xi), on (?) ξ ∈ R n have been established. The paper gives a pulse period differential system for solving periodic solution algorithm for optimal parameter selection problem (MP2). Finally, we apply the optimal parameters choice package in respect of cycle known equation, equations, unknown period and Impulsive Differential Equations cycle four numerical examples to illustrate the feasibility and effectiveness of our algorithm.
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