We consider the nonlinear neutral functional differential equation [r (t)[x(t) + b a p(t, µ)x(τ(t, µ))dµ] (n−1) ] + δ d c q(t, ξ)f (x(σ (t, ξ)))dξ = 0 with continuous arguments. We will develop oscillatory and asymptotic properties of the solutions. have studied the oscillation theory of second-order and higher-order neutral functional differential equations, in which the highest-order derivati...

(1) inf{‖f ‖p : f ∈ C [0, 1], f(ti) = ei, i = 1, . . . , m}, where ‖ · ‖p is the usual L [0, 1] norm, 1 ≤ p ≤ ∞, and to characterize f for which the above infimum is attained. If m ≤ n, then this problem has a simple solution. There are algebraic polynomials of degree at most n−1 satisfying the interpolation data, and any of these polynomials obviously solve our problem. If m > n then, in gener...

‎Second derivative general linear methods (SGLMs) as an extension‎ ‎of general linear methods (GLMs) have been introduced to improve‎ ‎the stability and accuracy properties of GLMs‎. ‎The coefficients of‎ ‎SGLMs are given by six matrices‎, ‎instead of four matrices for‎ ‎GLMs‎, ‎which are obtained by solving nonlinear systems of order and‎ ‎usually Runge--Kutta stability conditions‎. ‎In this p...