A second-order differential equation for a point charged particle

A RESEARCH NOTE ON THE SECOND ORDER DIFFERENTIAL EQUATION

Let U(t, ) be solution of the Dirichlet problem y''+( t-q(t))y= 0 - 1 t l y(-l)= 0 = y(x), with variabIe t on (-1, x), for fixed x, which satisfies the initial condition U(-1, )=0 , (-1, )=1. In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigen values has been investigated . Furthermore, the leading term of the asymptotic formula for ...

On Fuzzy Solution for Exact Second Order Fuzzy Differential Equation

In the present paper, the analytical solution for an exact second order fuzzy initial value problem under generalized Hukuhara differentiability is obtained. First the solution of first order linear fuzzy differential equation under generalized Hukuhara differentiability is investigated using integration factor methods in two cases. The second based on the type of generalized Hukuhara different...

A method for solving first order fuzzy differential equation

First - and Second - Order Charged Particle Optics

2 A General Firstand Second-Order Theory of Beam Transport Optics . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1 The Vector Differential Equation of Motion . . . . . . . . 2.2 The Coordinate System . . . . . . . . . . . . . . . . .’ . 2.3 Expanded Form of a Magnetic Field Having Median Plane Symmetry . . . . . . . . . . . . . . . . . . . . . . 2.4 Field Expansion to Second Order Only ....

Periodic solutions for a second order nonlinear functional differential equation

The second order nonlinear delay differential equation with periodic coefficients x ′′(t)+ p(t)x ′(t)+ q(t)x(t) = r(t)x ′(t − τ(t))+ f (t, x(t), x(t − τ(t))), t ∈ R is considered in this work. By using Krasnoselskii’s fixed point theorem and the contraction mapping principle, we establish some criteria for the existence and uniqueness of periodic solutions to the delay differential equation. c ...