A Noncollision Periodic Solution for N-Body Problems

Periodic Solutions for Circular Restricted N+ 1-Body Problems

and Applied Analysis 3 the critical point of f(q) in Λ ± is a periodic solution of Newtonian equation (5). Lemma 11. (1) (Gordon’s theorem [19]) Let x ∈ W 1,2 ([t 1 , t 2 ], R K ) and x(t 1 ) = x(t 2 ) = 0. Then for any a > 0, one has

Ewald and Multipole Methods for Periodic N-body Problems

Many realistic biomolecular simulations require use of periodic boundary conditions to create a surface-free environment for the molecule of interest and associated solvent molecules to interact. Electrostatic interactions are the principal computational cost of such simulations. We have implemented two codes: a parallel variant of an Ewald summation method which computes the eeect of innnite p...

Trigonometrically fitted two-step obrechkoff methods for the numerical solution of periodic initial value problems

In this paper, we present a new two-step trigonometrically fitted symmetric Obrechkoff method. The method is based on the symmetric two-step Obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve IVPs with periodic solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. The numeri...

Periodic solution for a delay nonlinear population equation with feedback control and periodic external source

In this paper, sufficient conditions are investigated for the existence of periodic (not necessarily positive) solutions for nonlinear several time delay population system with feedback control. Nonlinear system affected by an periodic external source is studied. Existence of a control variable provides  the extension of  some previous results obtained in other studies. We give a illustrative e...

Noncollision Singularities in the Newtonian N-body Problem: Results and Perspectives