A universal differential equation

A Universal Ordinary Differential Equation

An astonishing fact was established by Lee A. Rubel in 81: there exists a fixed non-trivial fourthorder polynomial differential algebraic equation (DAE) such that for any positive continuous function φ on the reals, and for any positive continuous function (t), it has a C∞ solution with |y(t) − φ(t)| < (t) for all t. Lee A. Rubel provided an explicit example of such a polynomial DAE. Other exam...

Universal Connection , Stochastic Differential Equation , Calculus on Loop Space

where FCb (Lx(M)) denotes the set of the smooth cylindrical functions and ∇(i) denotes the covariant derivative with respect to the i−th variable. Also τ(γ)t : TxM → Tγ(t)M is the stochastic parallel translation along γ. Among Riemannian connections, we restrict ourselves to the torsion skew symmetric (=TSS in short) connection, Namely the torsion T must satisfy that g(T (X, Y ), Y ) = 0. for a...

A method for solving first order fuzzy differential equation

A Note on Solving Prandtl's Integro-Differential Equation

A simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its ...

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 ...